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18 April 2025, Volume 34 Issue 5 Previous issue    Next issue

SPECIAL TOPIC — Advanced magnonics

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Magnon-magnon coupling in noncollinear synthetic antiferromagnets Tengfei Zhang(张腾飞), Quwen Wang(王曲文), Min Chen(陈敏), Jie Dong(董洁), Qian Zhao(赵乾), Zimu Li(李子木), Qingfang Liu(刘青芳), Jianbo Wang(王建波), and Jinwu Wei(魏晋武) Chin. Phys. B, 2025, 34 (5):  057201.  DOI: 10.1088/1674-1056/adb26b Abstract ( 224 )   HTML ( 0 )   PDF (2123KB) ( 146 )   We report a theoretical analysis of magnon-magnon coupling in a noncollinear magnetic sandwiched structure with interlayer exchange interaction, which consists of two ferromagnetic layers with perpendicular and in-plane magnetic anisotropy, respectively. Based on the Landau-Lifshitz equation, the spin wave dispersion is derived, and then the frequency gap is observed due to the magnon-magnon coupling effect induced by symmetry breaking. The influence of saturation magnetization, exchange coupling interaction, perpendicular magnetic anisotropy, and wave vector on the coupling strength is studied in detail. We find that the coupling strength is strongly dependent on the saturation magnetization and a small saturation magnetization can lead to strong coupling strength. By selecting the appropriate magnetic materials, the ultra-strong coupling regime can be achieved. The precession information in time domain is solved and the alternating change of the precession components in two ferromagnetic layers implies the exchange of energy and information.

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Nonreciprocal microwave-optical entanglement in Kerr-modified cavity optomagnomechanics Ming-Yue Liu(刘明月), Yuan Gong(龚媛), Jiaojiao Chen(陈姣姣), Yan-Wei Wang(王艳伟), and Wei Xiong(熊伟) Chin. Phys. B, 2025, 34 (5):  057202.  DOI: 10.1088/1674-1056/adb735 Abstract ( 176 )   HTML ( 0 )   PDF (1863KB) ( 58 )   Microwave-optical entanglement is essential for efficient quantum communication, secure information transfer, and integrating microwave and optical quantum systems to advance hybrid quantum technologies. In this work, we demonstrate how the magnon Kerr effect can be harnessed to generate and control nonreciprocal entanglement in cavity optomagnomechanics (COMM). This effect induces magnon frequency shifts and introduces pair-magnon interactions, both of which are tunable through the magnetic field direction, enabling nonreciprocal behavior. By adjusting system parameters such as magnon frequency detuning, we show that magnon-phonon, microwave-optical photon-photon, and optical photon-magnon entanglement can be nonreciprocally enhanced and rendered more robust against thermal noise. Additionally, the nonreciprocity of entanglement can be selectively controlled, and ideal nonreciprocal entanglement is achievable. This work paves the way for designing nonreciprocal quantum devices across the microwave and optical regimes, leveraging the unique properties of the magnon Kerr effect in COMM.

SPECIAL TOPIC — Quantum communication and quantum network

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Free-space discrete-variable quantum key distribution in a mountainous environment Xing-Ran Chen(陈星燃), Jian-Hong Shi(史建红), and Hai-Long Zhang(张海龙) Chin. Phys. B, 2025, 34 (5):  050301.  DOI: 10.1088/1674-1056/adbd25 Abstract ( 68 )   HTML ( 0 )   PDF (727KB) ( 42 )   Free-space quantum key distribution (QKD) offers broader geographical coverage and more flexible system deployment than fiber-based systems. However, the free-space environment is highly complex, and various attenuation factors can significantly reduce the key distribution efficiency or even lead to encoding failures. This paper discusses and analyzes the impact of turbulence and fog in mountainous environments on free-space discrete-variable quantum key distribution. Through numerical simulation, this study examines the effects of altitude and visibility on transmittance and turbulence intensity, finding that turbulence intensity decreases with increasing altitude while transmittance increases; improvements in visibility also lead to increased transmittance. Beam wandering due to turbulence is also dominant. Combining these factors, the effects on the total transmittance and the secret key rate are taken into consideration. Our work could provide a reference for the deployment of practical QKD systems in actual mountainous environments.

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Improving the performance of reference-frame-independent measurement-device-independent quantum key distribution in hybrid channels Yan-Mei Zhao(赵燕美), Chun Zhou(周淳), Xiao-Lei Jiang(姜晓磊), Yi-Fei Lu(陆宜飞), Yu Zhou(周雨), Hai-Tao Wang(汪海涛), Yang Wang(汪洋), Jia-Ji Li(李家骥), Yan-Yang Zhou(周砚扬), Hong-Wei Li(李宏伟), and Wan-Su Bao(鲍皖苏) Chin. Phys. B, 2025, 34 (5):  050302.  DOI: 10.1088/1674-1056/adbee4 Abstract ( 82 )   HTML ( 0 )   PDF (699KB) ( 58 )   The robustness of reference-frame-independent measurement-device-independent quantum key distribution (RFI-MDI-QKD) against detection system vulnerabilities and its tolerance to reference frame drifts make it an ideal choice for hybrid channels. However, the impact of atmospheric turbulence on transmittance fluctuations remains a significant challenge for enhancing the performance of RFI-MDI-QKD. In this paper, we apply prefixed-threshold real-time selection and advantage distillation techniques to RFI-MDI-QKD in a hybrid channels scenario. Then, we analytically derive formulas for secret key rate in hybrid channels. Simulation results show that our modified scheme has apparent advances in both maximum tolerant loss and secure key rate compared to the fiber-only channel. Specifically, the result demonstrates that the maximum transmission distance can be improved by 15 km and 28 km when $N={10}^{12}$ and ${10}^{11}$. Our work not only provides a more robust key distribution protocol but also establishes a solid theoretical foundation for enhancing the performance of RFI-MDI-QKD in hybrid channels.

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Multi-protocol quantum key distribution decoding chip Chun-Xue Zhang(张春雪), Jian-Guang Li(李建光), Yue Wang(王玥), Wei Chen(陈巍), Jia-Shun Zhang(张家顺), and Jun-Ming An(安俊明) Chin. Phys. B, 2025, 34 (5):  050303.  DOI: 10.1088/1674-1056/adb686 Abstract ( 61 )   HTML ( 0 )   PDF (1100KB) ( 34 )   Quantum key distribution (QKD) is a method for secure communication that utilizes quantum mechanics principles to distribute cryptographic keys between parties. Integrated photonics offer benefits such as compactness, scalability, energy efficiency and the potential for extensive integration. We have achieved BB84 phase encoding and decoding, time-bin phase QKD, and the coherent one-way (COW) protocol on a planar lightwave circuit (PLC) platform. At the optimal temperature, our chip successfully prepared quantum states, performed decoding and calculated the secure key rate of the time-bin phase-decoding QKD to be 80.46 kbps over a 20 km transmission with a quantum bit error rate (QBER) of 4.23%. The secure key rate of the COW protocol was 18.18 kbps, with a phase error rate of 3.627% and a time error rate of 0.377%. The uniqueness of this technology lies in its combination of high integration and protocol flexibility, providing an innovative solution for the development of future quantum communication networks.

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Unidirectional quantum private comparison based on quantum private query Hexiang Sun(孙鹤翔), Ding Xing(邢丁), Zhao Dou(窦钊), Jian Li(李剑), Xiubo Chen(陈秀波), and Lixiang Li(李丽香) Chin. Phys. B, 2025, 34 (5):  050308.  DOI: 10.1088/1674-1056/adc662 Abstract ( 56 )   HTML ( 0 )   PDF (2017KB) ( 49 )   Previous bidirectional quantum private comparison (BQPC) protocols cannot meet the requirements in some special application scenarios, where only one party needs to obtain the comparison results without a third party (TP), such as scenarios for authority surveys or healthcare data sharing. In addition to this, the BQPC protocol has the potential of information leakage in multiple comparisons. Therefore, we design a new unidirectional quantum private comparison (UQPC) protocol based on quantum private query (QPQ) protocols with ideal database security and zero failure probability (IDS-ZF), for the reason that they have excellent unidirectionality and security. Concretely, we design a UQPC protocol based on Wei et al.'s work [IEEE Transactions on Computers 67 2 (2017)] and it includes an authentication process to increase the resistance to outside attacks. Moreover, we generalize the protocol and propose a general model that can transform a QPQ protocol with or without the IDS-ZF property into a secure UQPC protocol. Finally, our study shows that protocols using our model are secure, practical, and have the IDS-ZF property.

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Dynamics of quantum discord and geometric quantum discord in multiqubit interacting system Xiao-Di Cheng(程晓迪), Ya-Jun Zheng(郑雅君), Meng-Jie Ran(冉梦杰), and Xiao-Yun Wang(王小云) Chin. Phys. B, 2025, 34 (5):  050309.  DOI: 10.1088/1674-1056/adca16 Abstract ( 70 )   HTML ( 0 )   PDF (2400KB) ( 26 )   Using quantum discord (QD) and geometric quantum discord (GQD), quantum correlation dynamics is investigated for two coupled qubits within a multiqubit interacting system in the zero-temperature bosonic reservoir, under both weak and strong qubit-reservoir coupling regimes. The multiqubit system is connected with either a common bosonic reservoir (CBR) or multiple independent bosonic reservoirs (IBRs). In the CBR case, our findings indicate that both QD and GQD can be strengthened by increasing the number of qubits in the multiqubit system. Furthermore, we study the steady state QD and GQD in the strong coupling regime, and find that the stable value in the long-time limit is determined exclusively by the number of qubits. The evolution period of QD and GQD gets longer as the dipole-dipole interaction (DDI) strength increases, which helps prolong the correlation time and thus preserves the quantum correlation under the weak coupling regime. Further analysis reveals notable differences between the CBR and IBRs scenarios. In the IBRs case, the decay of QD and GQD becomes slower compared to the CBR case, with both measures tending to zero at a reduced rate. Moreover, GQD consistently exhibits lower values than QD in both scenarios. These findings provide valuable insights into the selection of appropriate correlation measurement techniques for quantifying quantum correlations.

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Encoding converters for quantum communication networks Hua-Xing Xu(许华醒), Shao-Hua Wang(王少华), Ya-Qi Song(宋雅琪), Ping Zhang(张平), and Chang-Lei Wang(王昌雷) Chin. Phys. B, 2025, 34 (5):  050310.  DOI: 10.1088/1674-1056/adcdeb Abstract ( 64 )   HTML ( 0 )   PDF (537KB) ( 38 )   Quantum communication networks, such as quantum key distribution (QKD) networks, typically employ the measurement-resend mechanism between two users using quantum communication devices based on different quantum encoding types. To achieve direct communication between the devices with different quantum encoding types, in this paper, we propose encoding conversion schemes between the polarization bases (rectilinear, diagonal and circular bases) and the time-bin phase bases (two phase bases and time-bin basis) and design the quantum encoding converters. The theoretical analysis of the encoding conversion schemes is given in detail, and the basis correspondence of encoding conversion and the property of bit flip are revealed. The conversion relationship between polarization bases and time-bin phase bases can be easily selected by controlling a phase shifter. Since no optical switches are used in our scheme, the converter can be operated with high speed. The converters can also be modularized, which may be utilized to realize miniaturization in the future.

SPECIAL TOPIC — Computational programs in complex systems

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Programming guide for solving constraint satisfaction problems with tensor networks Xuanzhao Gao(高煊钊), Xiaofeng Li(李晓锋), and Jinguo Liu(刘金国) Chin. Phys. B, 2025, 34 (5):  050201.  DOI: 10.1088/1674-1056/adbee2 Abstract ( 95 )   HTML ( 0 )   PDF (1139KB) ( 89 )   Constraint satisfaction problems (CSPs) are a class of problems that are ubiquitous in science and engineering. They feature a collection of constraints specified over subsets of variables. A CSP can be solved either directly or by reducing it to other problems. This paper introduces the Julia ecosystem for solving and analyzing CSPs with a focus on the programming practices. We introduce some important CSPs and show how these problems are reduced to each other. We also show how to transform CSPs into tensor networks, how to optimize the tensor network contraction orders, and how to extract the solution space properties by contracting the tensor networks with generic element types. Examples are given, which include computing the entropy constant, analyzing the overlap gap property, and the reduction between CSPs.

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Trajectory tracking on the optimal path of two-dimensional quadratic barrier escaping Zengxuan Zhao(赵曾轩), Xiuying Zhang(张秀颖), Pengchen Zhao(赵鹏琛), Chunyang Wang(王春阳), Chunlei Xia(夏春雷), Mushtaq Rana Imran, and Joelous Malamula Nyasulu Chin. Phys. B, 2025, 34 (5):  050205.  DOI: 10.1088/1674-1056/adcb99 Abstract ( 75 )   HTML ( 0 )   PDF (1249KB) ( 49 )   The diffusion trajectory of a Brownian particle passing over the saddle point of a two-dimensional quadratic potential energy surface is tracked in detail according to the deep learning strategies. Generative adversarial networks (GANs) emanating in the category of machine learning (ML) frameworks are used to generate and assess the rationality of the data. While their optimization is based on the long short-term memory (LSTM) strategies. In addition to drawing a heat map, the optimal path of two-dimensional (2D) diffusion is simultaneously demonstrated in a stereoscopic space. The results of our simulation are completely consistent with the previous theoretical predictions.

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Planar: A software for exact decoding quantum error correction codes with planar structure Dongyang Feng(冯东阳), Hanyan Cao(曹涵彦), and Pan Zhang(张潘) Chin. Phys. B, 2025, 34 (5):  050311.  DOI: 10.1088/1674-1056/adcb26 Abstract ( 74 )   HTML ( 0 )   PDF (1720KB) ( 47 )   Quantum error correction is essential for realizing fault-tolerant quantum computing, where both the efficiency and accuracy of the decoding algorithms play critical roles. In this work, we introduce the implementation of the Planar algorithm, a software framework designed for fast and exact decoding of quantum codes with a planar structure. The algorithm first converts the optimal decoding of quantum codes into a partition function computation problem of an Ising spin glass model. Then it utilizes the exact Kac-Ward formula to solve it. In this way, Planar offers the exact maximum likelihood decoding in polynomial complexity for quantum codes with a planar structure, including the surface code with independent code-capacity noise and the quantum repetition code with circuit-level noise. Unlike traditional minimum-weight decoders such as minimum-weight perfect matching (MWPM), Planar achieves theoretically optimal performance while maintaining polynomial-time efficiency. In addition, to demonstrate its capabilities, we exemplify the implementation using the rotated surface code, a commonly used quantum error correction code with a planar structure, and show that Planar achieves a threshold of approximately $p_{\mathrm{u}\mathrm{c}}\approx 0.109$ under the depolarizing error model, with a time complexity scaling of $O(N^{0.69})$, where $N$ is the number of spins in the Ising model.

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Text-guided diverse-expression diffusion model for molecule generation Wenchao Weng(翁文超), Hanyu Jiang(蒋涵羽), Xiangjie Kong(孔祥杰), and Giovanni Pau Chin. Phys. B, 2025, 34 (5):  050701.  DOI: 10.1088/1674-1056/adbedd Abstract ( 72 )   HTML ( 0 )   PDF (864KB) ( 79 )   The task of molecule generation guided by specific text descriptions has been proposed to generate molecules that match given text inputs. Mainstream methods typically use simplified molecular input line entry system (SMILES) to represent molecules and rely on diffusion models or autoregressive structures for modeling. However, the one-to-many mapping diversity when using SMILES to represent molecules causes existing methods to require complex model architectures and larger training datasets to improve performance, which affects the efficiency of model training and generation. In this paper, we propose a text-guided diverse-expression diffusion (TGDD) model for molecule generation. TGDD combines both SMILES and self-referencing embedded strings (SELFIES) into a novel diverse-expression molecular representation, enabling precise molecule mapping based on natural language. By leveraging this diverse-expression representation, TGDD simplifies the segmented diffusion generation process, achieving faster training and reduced memory consumption, while also exhibiting stronger alignment with natural language. TGDD outperforms both TGM-LDM and the autoregressive model MolT5-Base on most evaluation metrics.

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Active learning attraction basins of dynamical system Xiao-Wei Cao(曹小尾), Xiao-Lei Ru(茹小磊), and Gang Yan(严钢) Chin. Phys. B, 2025, 34 (5):  058901.  DOI: 10.1088/1674-1056/adbede Abstract ( 135 )   HTML ( 0 )   PDF (2571KB) ( 56 )   Dynamical systems often exhibit multiple attractors representing significantly different functioning conditions. A global map of attraction basins can offer valuable guidance for stabilizing or transitioning system states. Such a map can be constructed without prior system knowledge by identifying attractors across a sufficient number of points in the state space. However, determining the attractor for each initial state can be a laborious task. Here, we tackle the challenge of reconstructing attraction basins using as few initial points as possible. In each iteration of our approach, informative points are selected through random seeding and are driven along the current classification boundary, promoting the eventual selection of points that are both diverse and enlightening. The results across various experimental dynamical systems demonstrate that our approach requires fewer points than baseline methods while achieving comparable mapping accuracy. Additionally, the reconstructed map allows us to accurately estimate the minimum escape distance required to transition the system state to a target basin.

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SFFSlib: A Python library for optimizing attribute layouts from micro to macro scales in network visualization Ke-Chao Zhang(张可超), Sheng-Yue Jiang(蒋升跃), and Jing Xiao(肖婧) Chin. Phys. B, 2025, 34 (5):  058903.  DOI: 10.1088/1674-1056/adcb98 Abstract ( 90 )   HTML ( 0 )   PDF (16393KB) ( 20 )   Complex network modeling characterizes system relationships and structures, while network visualization enables intuitive analysis and interpretation of these patterns. However, existing network visualization tools exhibit significant limitations in representing attributes of complex networks at various scales, particularly failing to provide advanced visual representations of specific nodes and edges, community affiliation attribution, and global scalability. These limitations substantially impede the intuitive analysis and interpretation of complex network patterns through visual representation. To address these limitations, we propose SFFSlib, a multi-scale network visualization framework incorporating novel methods to highlight attribute representation in diverse network scenarios and optimize structural feature visualization. Notably, we have enhanced the visualization of pivotal details at different scales across diverse network scenarios. The visualization algorithms proposed within SFFSlib were applied to real-world datasets and benchmarked against conventional layout algorithms. The experimental results reveal that SFFSlib significantly enhances the clarity of visualizations across different scales, offering a practical solution for the advancement of network attribute representation and the overall enhancement of visualization quality.

RAPID COMMUNICATION

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Shear viscosity of an ultracold Fermi gas in the BCS-BEC crossover Hot! Jing Min(闵靖), Xiangchuan Yan(严祥传), Da-Li Sun(孙大立), Lu Wang(王璐), Xin Xie(谢馨), Xizhi Wu(吴熙至), Shi-Guo Peng(彭世国), and Kaijun Jiang(江开军) Chin. Phys. B, 2025, 34 (5):  053103.  DOI: 10.1088/1674-1056/adc403 Abstract ( 224 )   HTML ( 2 )   PDF (610KB) ( 168 )   We report on the measurement of shear viscosity in an ultracold Fermi gas with variable temperatures and tunable interactions. A quadrupole mode excitation in an isotropic harmonic trap is used to quantify the shear viscosity of the quantum gas within the hydrodynamic regime. The shear viscosity of the system as a function of temperature has been investigated, and the results closely align with calculations in the high-temperature limit utilizing a new definition of the cutoff radius. Through an adiabatic sweep across the Bardeen-Cooper-Schrieffer (BCS) to Bose-Einstein condensate (BEC) crossover, we find that the minimum value of the shear viscosity, as a function of interaction strength, is significantly shifted toward the BEC side. Furthermore, the behavior of the shear viscosity is asymmetric on both sides of the location of the minimum.

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Resolving gravitational redshift with sub-millimeter height differences using spin-squeezed optical clocks Hot! Deshui Yu(于得水), Jia Zhang(张佳), Shougang Zhang(张首刚), Tiantian Shi(史田田), and Jingbiao Chen(陈景标) Chin. Phys. B, 2025, 34 (5):  054208.  DOI: 10.1088/1674-1056/adca1d Abstract ( 403 )   HTML ( 9 )   PDF (1517KB) ( 330 )   The phenomenon that a clock at a higher gravitational potential ticks faster than one at a lower potential, also known as gravitational redshift, is one of the classical tests of Einstein's theory of general relativity. Owing to their ultra-high accuracy and stability, state-of-the-art optical lattice clocks have enabled resolving the gravitational redshift with a millimeter-scale height difference. Further reducing the vertical inter-clock separation down to the sub-millimeter level and especially shortening the required measurement time may be achieved by employing spin squeezing. Here, we theoretically investigate the spin-squeezing-enhanced differential frequency comparison between two optical clocks within a lattice-trapped cloud of ${}^{171}$Yb atoms. The numerical results illustrate that for a sample of ${10}^4$ atoms, the atomic-collision-limited resolution of the vertical separation between two clocks can reach 0.48 mm, corresponding to a fractional gravitational redshift at the ${10}^{-20}$ level. In addition, the required averaging time may be reduced to less than one hundredth of that of conventional clocks with independent atoms. Our work opens a door to the future spin-squeezing-enhanced test of general relativity.

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Enhancing p-d hybridization via synergistic regulation of spatial and energetic orbital overlaps in Ba-doped LaNiO3 epitaxial films for oxygen evolution activity Hot! Yingjia Li(李莹嘉), Xiang Xu(徐翔), Xiaoyu Qiu(邱晓宇), Jie Tu(涂杰), Zijian Chen(陈子健), Yujie Zhou(周雨洁), Zhao Guan(关赵), Youyuan Zhang(张友圆), Wen-Yi Tong(童文旖), Shaohui Xu(徐少辉), Ni Zhong(钟妮), Pinghua Xiang(向平华), Chun-Gang Duan(段纯刚), and Binbin Chen(陈斌斌) Chin. Phys. B, 2025, 34 (5):  057101.  DOI: 10.1088/1674-1056/adc7f8 Abstract ( 225 )   HTML ( 1 )   PDF (2065KB) ( 82 )   The hybridization between oxygen 2p and transition-metal 3d states largely determines the electronic structure near the Fermi level and related functionalities of transition-metal oxides (TMOs). Considerable efforts have been made to manipulate the p-d hybridization in TMOs by tailoring the spatial orbital overlap via structural engineering. Here, we demonstrate enhanced p-d hybridization in Ba${}^{2+}$-doped LaNiO${}_3$ epitaxial films by simultaneously modifying both the spatial and energetic overlaps between the O-2p and Ni-3d orbitals. Combining x-ray absorption spectroscopy and first-principles calculations, we reveal that the enhanced hybridization stems from the synergistic effects of a reduced charge-transfer energy due to hole injection and an increased spatial orbital overlap due to straightening of Ni-O-Ni bonds. We further show that the enhanced p-d hybridization can be utilized to promote the oxygen evolution activity of LaNiO${}_3$. This work sheds new insights into the fine-tuning of the electronic structures of TMOs for enhanced functionalities.

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SR and NMR studies on the van der Waals cluster magnet Nb3Cl8 Hot! Lin Yang(杨林), Detong Wu(吴德桐), Xin Han(韩鑫), Jun Luo(罗军), Bo Liu(刘波), Xiaoyan Ma(马肖燕), Huiqian Luo(罗会仟), Jie Yang(杨杰), Bing Shen(沈冰), Rhea Stewart, Devashibhai Adroja, Youguo Shi(石友国), Rui Zhou(周睿), and Shiliang Li(李世亮) Chin. Phys. B, 2025, 34 (5):  057501.  DOI: 10.1088/1674-1056/adc667 Abstract ( 183 )   HTML ( 0 )   PDF (1417KB) ( 110 )   The van der Waals cluster magnet Nb${}_3$Cl${}_8$ has recently been shown to possibly host a quantum-spin-liquid ground state. The Nb ions in this compound form a breathing kagome structure, where the magnetic moment comes from three nearest Nb ions forming a molecular cluster with spin $1/2$. Previous bulk measurements including magnetic susceptibility and specific heat suggested the existence of spinon Fermi surfaces. Here we further probe the spin system by nuclear magnetic resonance (NMR) and muon spin rotation and relaxation (μSR) techniques. We confirm that there is no magnetic long-range order and the dynamical spin fluctuations persist down to 0.075 K. These results provide further evidence that Nb${}_3$Cl${}_8$ may host a quantum spin liquid.

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Scaling corrections in driven critical dynamics: Application to the two-dimensional dimerized quantum Heisenberg model Hot! Jing-Wen Liu(刘静雯), Shuai Yin(阴帅), and Yu-Rong Shu(舒玉蓉) Chin. Phys. B, 2025, 34 (5):  057502.  DOI: 10.1088/1674-1056/adc672 Abstract ( 238 )   HTML ( 0 )   PDF (799KB) ( 152 )   Driven critical dynamics in quantum phase transitions holds significant theoretical importance, and also has practical applications in fast-developing quantum devices. While scaling corrections have been shown to play important roles in fully characterizing equilibrium quantum criticality, their impact on nonequilibrium critical dynamics has not been extensively explored. In this work, we investigate the driven critical dynamics in a two-dimensional quantum Heisenberg model. We find that in this model the scaling corrections arising from both finite system size and finite driving rate must be incorporated into the finite-time scaling form in order to properly describe the nonequilibrium scaling behaviors. In addition, improved scaling relations are obtained from the expansion of the full scaling form. We numerically verify these scaling forms and improved scaling relations for different starting states using the nonequilibrium quantum Monte Carlo algorithm.

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Synergistic bulk and surface engineering via rapid quenching for high-performance Li-rich layered manganese oxide cathodes Hot! Xinyun Xiong(熊馨筠), Sichen Jiao(焦思晨), Qinghua Zhang(张庆华), Luyao Wang(王璐瑶), Kun Zhou(周坤), Bowei Cao(曹博维), Xilin Xu(徐熙林), Xiqian Yu(禹习谦), and Hong Li(李泓) Chin. Phys. B, 2025, 34 (5):  058201.  DOI: 10.1088/1674-1056/adc673 Abstract ( 164 )   HTML ( 3 )   PDF (8343KB) ( 127 )   Lithium-rich manganese-based cathodes (LRMs) have garnered significant attention as promising candidates for high-energy-density batteries due to their exceptional specific capacity exceeding 300 mAh/g, achieved through synergistic anionic and cationic redox reactions. However, these materials face challenges including oxygen release-induced structural degradation and consequent capacity fading. To address these issues, strategies such as surface modification and bulk phase engineering have been explored. In this study, we developed a facile and cost-effective quenching approach that simultaneously modifies both surface and bulk characteristics. Multi-scale characterization and computational analysis reveal that rapid cooling partially preserves the high-temperature disordered phase in the bulk structure, thereby enhancing the structural stability. Concurrently, Li${}^{+}$/H${}^{+}$ exchange at the surface forms a robust rock-salt/spinel passivation layer, effectively suppressing oxygen evolution and mitigating interfacial side reactions. This dual modification strategy demonstrates a synergistic stabilization effect. The enhanced oxygen redox activity coexists with the improved structural integrity, leading to superior electrochemical performance. The optimized cathode delivers an initial discharge capacity approaching 307.14 mAh/g at 0.1 C and remarkable cycling stability with 94.12% capacity retention after 200 cycles at 1 C. This study presents a straightforward and economical strategy for concurrent surface-bulk modification, offering valuable insights for designing high-capacity LRM cathodes with extended cycle life.

GENERAL

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Study and application of solitary wave propagation at fractional order of time based on SPH method Luyang Ma(马璐阳), Rahmatjan Imin(热合买提江·依明), and Azhar Halik(艾孜海尔·哈力克) Chin. Phys. B, 2025, 34 (5):  050202.  DOI: 10.1088/1674-1056/adbd2a Abstract ( 58 )   HTML ( 0 )   PDF (5550KB) ( 10 )   A meshless particle method based on the smoothed particle hydrodynamics (SPH) method is first proposed for the numerical prediction of physical phenomena of nonlinear solitary wave propagation and complex phenomena arising from the inelastic interactions of solitary waves. The method is a fully discrete implicit scheme. This method does not rely on a grid, avoids the need to solve for derivatives of kernel functions, and makes the calculation more convenient. Additionally, the unique solvability of the proposed implicit scheme is proved. To verify the effectiveness and flexibility of the proposed method, we apply it to solving various time fractional nonlinear Schrödinger equations (TF-NLSE) on both regular and irregular domains. This mainly includes general or coupled TF-NLSE with or without analytical solutions. Moreover, the proposed method is compared with the existing methods. Through examples, it has been verified that this method can effectively predict complex propagation phenomena generated by the collision of nonlinear solitary waves, such as the collapse phenomenon of solitary waves with increasing fractional-order parameters. Research results indicate that this method provides a new and effective meshless method for predicting the propagation of nonlinear solitary waves, which can better simulate TF-NLSE in complex domains.

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Adaptive multi-stable stochastic resonance assisted by neural network and physical supervision Xucan Li(李栩灿), Deming Nie(聂德明), Ming Xu(徐明), and Kai Zhang(张凯) Chin. Phys. B, 2025, 34 (5):  050203.  DOI: 10.1088/1674-1056/adbd28 Abstract ( 61 )   HTML ( 2 )   PDF (2023KB) ( 56 )   Stochastic resonance can utilize the energy of noise to enhance weak frequency characteristic. This paper proposes an adaptive multi-stable stochastic resonance method assisted by the neural network (NN) and physics supervision (directly numerical simulation of the physical system). Different from traditional adaptive algorithm, the evaluation of the objective function (i.e., fitness function) in iteration process of adaptive algorithm is through a trained neural network instead of the numerical simulation. It will bring a dramatically reduction in computation time. Considering predictive bias from the neural network, a secondary correction procedure is introduced to the reevaluate the top performers and then resort them in iteration process through physics supervision. Though it may increase the computing cost, the accuracy will be enhanced. Two examples are given to illustrate the proposed method. For a classical multi-stable stochastic resonance system, the results show that the proposed method not only amplifies weak signals effectively but also significantly reduces computing time. For the detection of weak signal from outer ring in bearings, by introducing a variable scale coefficient, the proposed method can also give a satisfactory result, and the characteristic frequency of the fault signal can be extracted correctly.

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Exactly solvable models for non-Hermitian systems under nonadiabatic quench dynamics Kangyi Hu(胡康溢), Menghua Deng(邓孟华), and Fuxiang Li(李福祥) Chin. Phys. B, 2025, 34 (5):  050204.  DOI: 10.1088/1674-1056/adbd26 Abstract ( 68 )   HTML ( 1 )   PDF (1404KB) ( 46 )   Due to the nonunitary time evolution and possibly complex energy eigenvalues in non-Hermitian systems, it is still under debate how to properly deal with the dynamics of time-dependent non-Hermitian Hamiltonian. Recently a quantum metric framework has been proposed to study the dynamics of generated defects of a non-Hermitian system under linear quench. Here, we provide an explicit expression for the endowed Hamiltonian under quantum metric for a general two-level non-Hermitian system. Then we propose two exactly solvable models for the study of nonadiabatic dynamics of non-Hermitian systems, and analyze the defect production using the metric method. We find that, in contrast to the direct normalization method, the metric method can reproduce the symmetry of generated defects. The power-law scaling of generated defects with respect to quench time is also obtained.

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Investigating maximal steered coherence under the common impacts of reservoir and noise Ling-Ling Xing(邢玲玲), Huan Yang(杨欢), and Gang Zhang(张刚) Chin. Phys. B, 2025, 34 (5):  050304.  DOI: 10.1088/1674-1056/adbbc2 Abstract ( 65 )   HTML ( 0 )   PDF (606KB) ( 16 )   Maximal steered coherence (MSC) is a noteworthy resource measure in the field of quantum information, and it is defined under the framework of coherence measure and the formalism of quantum steering ellipsoids (QSEs). Here, we explore the MSC of a two-qubit X state under the common influences of reservoir and noise. The results disclose that the introduction of auxiliary qubits can give rise to enhancement of the MSC in both the strong and weak coupling regimes. Moreover, more auxiliary qubits can decrease the oscillation period of the MSC, and also suppress the oscillation amplitude of the MSC in the strong coupling regime. In contrast, the increases in auxiliary qubits result in the oscillation of the MSC for the setting of the initially weak coupling regime. Of particular interest is that the improvement effects of more auxiliary qubits on the MSC in the initially weak coupling regime are significantly stronger than that in the initially strong coupling regime.

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Distributed quantum circuit partitioning and optimization based on combined spectral clustering and search tree strategies Zilu Chen(陈子禄), Zhijin Guan(管致锦), Shuxian Zhao(赵书娴), and Xueyun Cheng(程学云) Chin. Phys. B, 2025, 34 (5):  050305.  DOI: 10.1088/1674-1056/adbada Abstract ( 77 )   HTML ( 0 )   PDF (653KB) ( 12 )   In the current noisy intermediate-scale quantum (NISQ) era, a single quantum processing unit (QPU) is insufficient to implement large-scale quantum algorithms; this has driven extensive research into distributed quantum computing (DQC). DQC involves the cooperative operation of multiple QPUs but is concurrently challenged by excessive communication complexity. To address this issue, this paper proposes a quantum circuit partitioning method based on spectral clustering. The approach transforms quantum circuits into weighted graphs and, through computation of the Laplacian matrix and clustering techniques, identifies candidate partition schemes that minimize the total weight of the cut. Additionally, a global gate search tree strategy is introduced to meticulously explore opportunities for merged transfer of global gates, thereby minimizing the transmission cost of distributed quantum circuits and selecting the optimal partition scheme from the candidates. Finally, the proposed method is evaluated through various comparative experiments. The experimental results demonstrate that spectral clustering-based partitioning exhibits robust stability and efficiency in runtime in quantum circuits of different scales. In experiments involving the quantum Fourier transform algorithm and Revlib quantum circuits, the transmission cost achieved by the global gate search tree strategy is significantly optimized.

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A graph neural network and multi-task learning-based decoding algorithm for enhancing XZZX code stability in biased noise Bo Xiao(肖博), Zai-Xu Fan(范在旭), Hui-Qian Sun(孙汇倩), Hong-Yang Ma(马鸿洋), and Xing-Kui Fan(范兴奎) Chin. Phys. B, 2025, 34 (5):  050306.  DOI: 10.1088/1674-1056/adbadb Abstract ( 70 )   HTML ( 1 )   PDF (1844KB) ( 88 )   Quantum error correction is a technique that enhances a system's ability to combat noise by encoding logical information into additional quantum bits, which plays a key role in building practical quantum computers. The $XZZX$ surface code, with only one stabilizer generator on each face, demonstrates significant application potential under biased noise. However, the existing minimum weight perfect matching (MWPM) algorithm has high computational complexity and lacks flexibility in large-scale systems. Therefore, this paper proposes a decoding method that combines graph neural networks (GNN) with multi-classifiers, the syndrome is transformed into an undirected graph, and the features are aggregated by convolutional layers, providing a more efficient and accurate decoding strategy. In the experiments, we evaluated the performance of the $XZZX$ code under different biased noise conditions ($\mathrm{b}\mathrm{i}\mathrm{a}\mathrm{s}=1$, 20, 200) and different code distances ($d=3$, 5, 7, 9, 11). The experimental results show that under low bias noise ($\mathrm{b}\mathrm{i}\mathrm{a}\mathrm{s}=1$), the GNN decoder achieves a threshold of 0.18386, an improvement of approximately 19.12% compared to the MWPM decoder. Under high bias noise ($\mathrm{b}\mathrm{i}\mathrm{a}\mathrm{s}=200$), the GNN decoder reaches a threshold of 0.40542, improving by approximately 20.76%, overcoming the limitations of the conventional decoder. They demonstrate that the GNN decoding method exhibits superior performance and has broad application potential in the error correction of $XZZX$ code.

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Single-scattering characteristics of melting ice crystal particles in the millimeter-wave band Xue-Hai Zhang(张学海), Wen-Bo Liu(刘文博), Xin-Hui Zhang(张欣慧), He-Li Wei(魏合理), Wei-Dong Li(李卫东), Jin-Long Duan(段金龙), Shu-Guang Zou(邹曙光), Jia Liu(刘佳), and Cong-Ming Dai(戴聪明) Chin. Phys. B, 2025, 34 (5):  050307.  DOI: 10.1088/1674-1056/adbd23 Abstract ( 65 )   HTML ( 0 )   PDF (892KB) ( 34 )   The melting process of ice crystal particles has a significant effect on weather forecasting and global climate. Millimeter waveband is an excellent frequency range for exploring the optical characteristics of ice crystal particles. In this study, a new nonspherical and inhomogeneous ice crystal particle model is built based on the melting process of ice crystal particles. The single-scattering characteristics of ice crystal particles with different frequencies, sizes, shapes and ice crystal content (ICC) are investigated using the discrete dipole approximation (DDA) method. The results show that the single-scattering characteristics of ice crystal particles are closely related to the equivalent radius, frequency, morphology and mixing state. The single-scattering properties of the particles change regularly with the melting process of the ice crystal particles. Specifically, in the early stage of the ice crystal particle melting process, the single-scattering characteristics of ice crystal particles change significantly. With further melting, the change in the single-scattering characteristics of ice crystal particles gradually slows down when the ICC is less than 0.5. The results also show that in the early stage of the melting process, the shape of the ice crystal particles has a huge influence on the single-scattering characteristics of the particles, and in the late stage of the melting process, the single-scattering characteristics of the ice crystal particles are basically independent of the morphology of the ice crystal nuclei. This means that the influence of the morphology of the ice crystal nuclei needs to be considered in phases when simulating the scattering characteristics of the melting ice crystal particles. In summary, the results of this study should improve our understanding of the effect of size parameter, morphology and mixing state on the millimeter-wave scattering characteristics of ice clouds during the melting process and provide a reference for the remote sensing inversion of ice cloud microphysical characteristics

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Effects of potential field delay and coupling delay on collective behavior of a fractional-order coupled system in a dichotomous fluctuating potential Yangfan Zhong(钟扬帆), Xi Chen(陈熙), Maokang Luo(罗懋康), and Tao Yu(蔚涛) Chin. Phys. B, 2025, 34 (5):  050501.  DOI: 10.1088/1674-1056/adbd15 Abstract ( 47 )   HTML ( 0 )   PDF (5058KB) ( 12 )   The collective dynamic of a fractional-order globally coupled system with time delays and fluctuating frequency is investigated. The power-law memory of the system is characterized using the Caputo fractional derivative operator. Additionally, time delays in the potential field force and coupling force transmission are both considered. Firstly, based on the delay decoupling formula, combined with statistical mean method and the fractional-order Shapiro-Loginov formula, the ``statistic synchronization'' among particles is obtained, revealing the statistical equivalence between the mean field behavior of the system and the behavior of individual particles. Due to the existence of the coupling delay, the impact of the coupling force on synchronization exhibits non-monotonic, which is different from the previous monotonic effects. Then, two kinds of theoretical expression of output amplitude gains $G$ and $\overline{G}$ are derived by time-delay decoupling formula and small delay approximation theorem, respectively. Compared to $\overline{G}$, $G$ is an exact theoretical solution, which means that $G$ is not only more accurate in the region of small delay, but also applies to the region of large delay. Finally, the study of the output amplitude gain $G$ and its resonance behavior are explored. Due to the presence of the potential field delay, a new resonance phenomenon termed ``periodic resonance'' is discovered, which arises from the periodic matching between the potential field delay and the driving frequency. This resonance phenomenon is analyzed qualitatively and quantitatively, uncovering undiscovered characteristics in previous studies.

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Resonant tunneling diode cellular neural network with memristor coupling and its application in police forensic digital image protection Fei Yu(余飞), Dan Su(苏丹), Shaoqi He(何邵祁), Yiya Wu(吴亦雅), Shankou Zhang(张善扣), and Huige Yin(尹挥戈) Chin. Phys. B, 2025, 34 (5):  050502.  DOI: 10.1088/1674-1056/adb8bb Abstract ( 94 )   HTML ( 0 )   PDF (2543KB) ( 55 )   Due to their biological interpretability, memristors are widely used to simulate synapses between artificial neural networks. As a type of neural network whose dynamic behavior can be explained, the coupling of resonant tunneling diode-based cellular neural networks (RTD-CNNs) with memristors has rarely been reported in the literature. Therefore, this paper designs a coupled RTD-CNN model with memristors (RTD-MCNN), investigating and analyzing the dynamic behavior of the RTD-MCNN. Based on this model, a simple encryption scheme for the protection of digital images in police forensic applications is proposed. The results show that the RTD-MCNN can have two positive Lyapunov exponents, and its output is influenced by the initial values, exhibiting multistability. Furthermore, a set of amplitudes in its output sequence is affected by the internal parameters of the memristor, leading to nonlinear variations. Undoubtedly, the rich dynamic behaviors described above make the RTD-MCNN highly suitable for the design of chaos-based encryption schemes in the field of privacy protection. Encryption tests and security analyses validate the effectiveness of this scheme.

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A novel non-autonomous hyperchaotic map based on discrete memristor parallel connection Weiping Wu(吴伟平), Mengjiao Wang(王梦蛟), and Qigui Yang(杨启贵) Chin. Phys. B, 2025, 34 (5):  050503.  DOI: 10.1088/1674-1056/adb8bc Abstract ( 48 )   HTML ( 0 )   PDF (3982KB) ( 12 )   Since the method of discretizing memristors was proposed, discrete memristors (DMs) have become a very important topic in recent years. However, there has been little research on non-autonomous discrete memristors (NDMs) and their applications. Therefore, in this paper, a new NDM is constructed, and a non-autonomous hyperchaotic map is proposed by connecting this non-autonomous memristor in parallel with an autonomous memristor. This map exhibits complex dynamical behaviors, including infinitely many fixed points, initial-boosted attractors, initial-boosted bifurcations, and the size of the attractors being controlled by the initial value. In addition, a simple pseudo-random number generator (PRNG) was designed using the non-autonomous hyperchaotic map, and the pseudo-random numbers (PRNs) generated by it were tested using the National Institute of Standards and Technology (NIST) SP800-22 test suite. Finally, the non-autonomous hyperchaotic map is implemented on the STM32 hardware experimental platform.

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Deep learning-enabled inverse design of polarization-selective structural color based on coding metasurface Haolin Yang(杨昊霖), Bo Ni(倪波), Junhong Guo(郭俊宏), Hua Zhou(周华), and Jianhua Chang(常建华) Chin. Phys. B, 2025, 34 (5):  050702.  DOI: 10.1088/1674-1056/adb94a Abstract ( 58 )   HTML ( 0 )   PDF (1807KB) ( 32 )   Structural colors based on metasurfaces have very promising applications in areas such as optical image encryption and color printing. Herein, we propose a deep learning-enabled reverse design of polarization-selective structural color based on coding metasurface. In this study, the long short-term memory (LSTM) neural network is presented to enable the forward and inverse mapping between coding metasurface structure and corresponding color. The results show that the method can achieve 98% accuracy for the forward prediction of color and 93% accuracy for the inverse design of the structure. Moreover, a cascaded architecture is adopted to train the inverse neural network model, which can solve the non-uniqueness problem of the polarization-selective color reverse design. This study provides a new path for the application and development of structural colors.

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A high light-yield neutron scintillator based on Ce3+-doped lithium glass Rui-Qiang Song(宋瑞强), Chuang Liu(刘闯), Yi-Yang Long(龙逸洋), Ji-Feng Han(韩纪锋), Jing Ren(任晶), and Sen Qian(钱森) Chin. Phys. B, 2025, 34 (5):  050703.  DOI: 10.1088/1674-1056/adb94b Abstract ( 267 )   HTML ( 0 )   PDF (689KB) ( 95 )   The development of low-cost and highly efficient thermal neutron detection materials to substitute the rare and expensive ${}^3$He gas is important for applications requiring thermal neutron detection. Lithium-based glass (Li glass) is a promising candidate due to its simple fabrication process and low cost. This paper reports the optical properties and scintillation performance of a new Ce${}^{3+}$-doped Li glass, whose luminescence efficiency is significantly enhanced with a light yield of about 4770 ph/MeV, which is about 54% of that of BGO crystal, and the energy resolution is 14.5% for 662 keV gamma rays. The Ce${}^{3+}$-doped Li glass shows a high light yield of about 7058 ph/neutron, which is about 1.18 times that of the reference GS20 glass. The Ce${}^{3+}$-doped Li glass exhibits stronger gamma ray suppression capability compared to GS20 glass samples. Further optimizing the Ce${}^{3+}$ concentration and ${}^6$Li content is expected to achieve much superior neutron detection efficiency, positioning it as a promising alternative to ${}^3$He gas for efficient thermal neutron detection.

ATOMIC AND MOLECULAR PHYSICS

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Detailed discussion of discrepancy between theoretical and observed spectral lines in Kr-like W38+ based on advanced consideration of core electron correlations Guo-Qing Peng(彭国庆), Kai Wang(王凯), Jun Yan(颜君), and Wei Kang(康炜) Chin. Phys. B, 2025, 34 (5):  053101.  DOI: 10.1088/1674-1056/adbdbe Abstract ( 152 )   HTML ( 0 )   PDF (689KB) ( 23 )   For the observed line at 799.23 Å in tungsten EBIT experiment, which was assigned to be ${}^3{\mathrm{F}}_4^{\mathrm{o}}{-}^3{\mathrm{F}}_3^{\mathrm{o}}$ $([\mathrm{A}\mathrm{r}]4{\mathrm{s}}^{2}4{\mathrm{p}}^{5}4\mathrm{d})$ of W${}^{38+}$ ion, there were noticeable deviations for most calculated wavelengths from the measured value. To clarify this issue, we carry out an extensive calculation for energy levels and transition properties of W${}^{38+}$ ion using the multi-configuration Dirac-Hartree-Fock and relativistic configuration interaction method, in which more deeper inner core electron correlations are included, and different forms of Breit interaction as well as quantum electrodynamics corrections are investigated. It is found that the inner core electron correlations can affect the total energy of levels, while only slightly modify the excited energy of levels in 4s${}^2$4p${}^5$4d complex. The present calculated wavelengths agree with the corresponding measured values excellently except the line at 799.23 Å. Thus we are strongly suspicious this line should be misidentified, and suggest that new experiment with higher resolution and spectra analysis based on more accurate atomic data should be performed for W${}^{38+}$ ion.

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Photophysical property of fluorescent guanine analogs for selectively recognizing acetylated cytosine: A theoretical study Xiaolin Chen(陈晓琳), Xixi Cui(崔习习), Yongkang Lyu(吕永康), Chenyang Zhang(张晨阳), Changzhe Zhang(张常哲), and Qingtian Meng(孟庆田) Chin. Phys. B, 2025, 34 (5):  053102.  DOI: 10.1088/1674-1056/adb8ba Abstract ( 140 )   HTML ( 0 )   PDF (1667KB) ( 29 )   The photophysical properties of fluorescent nucleobase analogs play a crucial role in nucleic acids detection and the investigation of their structural and functional characteristics. In this study, we computationally designed a series of quasi-intrinsic fluorescent probes according to natural guanine (G) for selectively identifying covalent N${}^4$-acetylcytosine (4acC), a base that is highly correlated with active transcription and gene expression. This work aims to gain insight into the role of 4acC in biological regulation with minimal perturbation to the native DNA structure. The results indicate that these G-analogs possess extended $\pi$-conjugation in comparison with the natural guanine, which could yield efficient fluorescence emission and red-shifted absorption. Especially, the 8-thienyl-2'-deoxyguanosine (ThG) exhibits the highest fluorescence intensity and avoids self-absorption on account of the large Stokes shifts (> 67 nm). What is more, the fluorescence of ThG is unaffected to base pairing with natural cytosine, while the obvious fluorescence quenching is observed by virtue of the excited state intermolecular charge transfer after pairing with 4acC, so it is supposed as a promising biosensor for monitoring the fluorescence changes in the absence or presence of the 4acC. Additionally, the impact of binding deoxyribose on photophysical properties is explored to guarantee the biological applicability of the bright G-analogs in real environment.

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Alignment-dependent ionization of molecules in near-circularly polarized intense laser fields Jie Liu(刘洁), Yong-Kang Zhang(张永康), and Xiao-Lei Hao(郝小雷) Chin. Phys. B, 2025, 34 (5):  053201.  DOI: 10.1088/1674-1056/adbdc2 Abstract ( 139 )   HTML ( 1 )   PDF (2240KB) ( 59 )   The alignment-dependent photoelectron spectrum is a valuable tool for mapping out the electronic structure of molecular orbitals. However, this approach may not be applicable to all molecules, such as CO${}_2$, as the ionization process in a linearly polarized laser field involves contributions from orbitals other than the highest occupied molecular orbital (HOMO). Here, we conducted a theoretical investigation into the ionization process of N${}_2$ and CO${}_2$ in near-circularly polarized laser field using the Coulomb-corrected strong-field approximation (CCSFA) method for molecules. In particular, we introduced a generalized dressed state into the CCSFA method in order to account for the impact of the laser field on the molecular initial state. The simulated alignment-dependent photoelectron momentum distribution (PMD) of the two molecules exhibited markedly disparate behaviors, which were in excellent agreement with the previous experimental observations reported in [Phys. Rev. A 102, 013117 (2020)]. Our findings indicate that under a near-circularly polarized laser field, the alignment-dependent PMD of molecules is primarily sourced from the HOMO, in contrast to the situation under a linearly polarized laser field. Moreover, a satisfactory correlation between the alignment-dependent angular distribution and the orbital symmetry was observed, which suggests an effective approach for molecular orbital imaging.

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Rotational dynamics of neutral O2 driven by linearly, elliptically and circularly polarized femtosecond pulsed lasers Ting Xu(许婷), Jin-Peng Ma(马金鹏), Xiao-Qing Hu(胡晓青), Yin-Song Tang(唐寅淞), Si-Qi Pei(裴思琪), Cong-Cong Jia(贾聪聪), Yong-Wu(吴勇), and Jian-Guo Wang(王建国) Chin. Phys. B, 2025, 34 (5):  053301.  DOI: 10.1088/1674-1056/adbeea Abstract ( 179 )   HTML ( 0 )   PDF (1193KB) ( 89 )   Rotational dynamics simulations of neutral O${}_2$ molecules driven by linearly, elliptically and circularly polarized femtosecond pulsed lasers are carried out using a full quantum time-dependent wave packet evolution method. Here, the direction of laser propagation is set along the z axis, and the polarization plane is restricted to the xy plane. The results indicate that the alignment of O${}_2$ molecules in the z direction is weakly affected by varying the ellipticity when the total laser intensity is held constant. For rotation within the xy plane, the linearly polarized laser significantly excites rotational motion, with the degree of excitation increasing as the ellipticity increases. In contrast, under the influence of a circularly polarized laser, the angular distribution of O${}_2$ molecules in the xy plane remains isotropic. Additionally, the effects of the initial rotational quantum number, the temperature of the O${}_2$ molecules and the nuclear spin on laser-induced alignment are discussed.

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Pure hyperfine spectra of KRb in its vibronic ground state: Towards the determination of nuclear spin-spin interaction Qi Ouyang(欧阳琪), Xu-Ping Shao(邵旭萍), Yun-Xia Huang(黄云霞), and Xiao-Hua Yang(杨晓华) Chin. Phys. B, 2025, 34 (5):  053302.  DOI: 10.1088/1674-1056/adbdc1 Abstract ( 111 )   HTML ( 0 )   PDF (554KB) ( 9 )   The Zeeman-hyperfine-rotational spectra of ${}^{40}$K${}^{87}$Rb within its vibronic ground state at a magnetic field of 545.9 G are investigated by adopting the latest molecular constants available, and the results are in good agreement with the experimental observation made by Ospelkaus et al. [Phys. Rev. Lett. 104 030402 (2010)]. However, the calculated spectra generally shift by $-3.6$ kHz from the experimental ones, which implies the inaccuracy of the effective rotational constant. Therefore, we refit the spectra and obtain a new $B_{\mathrm{e}\mathrm{f}\mathrm{f}}=1113952(1)$ kHz, which reduces the overall root-mean-square deviation from 10.8 kHz to 7.9 kHz. Furthermore, the pure hyperfine spectra within the $J=0$ and 1 rotational states are simulated. We find that the scalar nuclear spin-spin interaction dominates the hyperfine splitting of $J=0$ despite it being slightly indirectly affected by the nuclear electric quadruple interaction due to the rotational perturbation, while the nuclear electric quadrupole interactions dominate the splitting, and the scalar and tensor nuclear spin-spin interactions also affect the splitting of $J=1$. The detailed hyperfine-rotational perturbations are studied. Therefore, the scalar and tensor nuclear spin-spin interaction constants can be precisely determined by simultaneously measuring the pure hyperfine radio-frequency spectra of the $J=0$ and 1 states in the vibronic ground state.

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Ultracold atomic absorption imaging system in high magnetic fields Yuying Chen(陈玉莹), Zhengxi Zhang(张正熙), Hongmian Shui(税鸿冕), Yun Liang(梁芸), Fansu Wei(魏凡粟), and Xiaoji Zhou(周小计) Chin. Phys. B, 2025, 34 (5):  053303.  DOI: 10.1088/1674-1056/adc7f6 Abstract ( 108 )   HTML ( 0 )   PDF (1607KB) ( 17 )   Absorption imaging is a fundamental technique for quantitatively extracting information from ultracold atom experiments. Since ultracold ${}^6\text{Li}$ atoms are prepared and detected under high magnetic fields, the suitable detuning of the probe light can reach the GHz level compared to zero-field imaging. Therefore, based on the energy level structure of ${}^6\text{Li}$ atoms and the requirements of subsequent experiments, we design a high-field imaging system with a large frequency range and good robustness, starting from the rationality of the optical layout design and employing offset locking techniques. This imaging system covers the entire crossover region from Bose-Einstein condensate to Bardeen-Cooper-Schrieffer (BEC-BCS) and realizes free switching between zero-field and high-field imaging. Additionally, by introducing a proportionality coefficient to correct for the intensity fluctuations of the probe light, we mitigate its disturbance on the statistical measurement of particle numbers in the experiment. This work not only provides a design reference for other quantum gas experiments requiring absorption imaging under strong bias magnetic fields, but also serves as an important reference for improving the imaging performance.

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Fragmentation dynamics of nitric oxide induced by low-energy heavy ions Zhixin Li(李志欣), Kaizhao Lin(林楷钊), Xiaolong Zhu(朱小龙), Zhiliang Li(李志亮), Hang Yuan(苑航), Yong Gao(高永), Dalong Guo(郭大龙), Dongmei Zhao(赵冬梅), Shaofeng Zhang(张少锋), and Xinwen Ma(马新文) Chin. Phys. B, 2025, 34 (5):  053401.  DOI: 10.1088/1674-1056/adbdc0 Abstract ( 157 )   HTML ( 0 )   PDF (685KB) ( 15 )   We study the fragmentation of NO${}^{q+}$ ($q=2$,3) molecular ions produced by collisions between 96 keV O${}^{6+}$ ions and neutral nitric oxide (NO) molecules, using the cold target recoil ion momentum spectrometer (COLTRIMS). The kinetic energy release (KER) for various dissociation channels is obtained. For the channel NO${}^{2+}\to {\mathrm{N}}^{+}+{\mathrm{O}}^{+}$, double-electron capture followed by autoionization of the projectile ions is the dominant process, which can be explained by the recapture of loosely bound electrons into highly excited states of the target. For NO${}^{3+}$ trication, two dissociation channels, i.e., (a) N${}^{+}+{\mathrm{O}}^{2+}$ and (b) N${}^{2+}+{\mathrm{O}}^{+}$, are observed, where channel (b) is the dominant channel. Moreover, for dissociation channels originating from the same parent molecular ion, the dissociation channel with a higher charge for the oxygen ion fragment exhibits a higher most probable KER, which is consistent with studies of CO fragmentation by Rajput et al. Additionally, it is observed that as capture stability increases, the average KER shifts to higher values.

ELECTROMAGNETISM, OPTICS, ACOUSTICS, HEAT TRANSFER, CLASSICAL MECHANICS, AND FLUID DYNAMICS

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Impact of free electron laser coherence on imaging quality Shuang Wei(魏爽), Shuang Gong(龚爽), Yang Bu(步扬), and Zi-Jian Song(宋子健) Chin. Phys. B, 2025, 34 (5):  054201.  DOI: 10.1088/1674-1056/adb734 Abstract ( 156 )   HTML ( 1 )   PDF (1571KB) ( 54 )   The high temporal and spatial coherence of free electron lasers (FELs) reduces the uniformity of the illumination field, leading to scattering effects that blur the edges of patterns, resulting in diminished accuracy and clarity. Traditional imaging models regard the light source as fully incoherent, making it difficult to assess the impact of partially coherent light fields on imaging. If FELs are used in imaging systems, their coherence must be considered. To address this issue, this study explores the relationship between coherence, imaging quality and speckle contrast through a simulation method based on random phases. The method divides the light beam into temporal and spatial coherence cells, analyzes their interactions, and simulates imaging results under different coherence conditions. Additionally, speckle patterns for various illumination modes are calculated to evaluate their effects on speckle contrast and illumination uniformity. The results indicate that under different illumination modes, illumination uniformity decreases as coherence increases, while speckle contrast increases with higher coherence. In terms of imaging quality, higher coherence leads to an increase in both line edge roughness (LER) and line width roughness (LWR), thereby reducing the imaging quality. Additionally, the narrower the line width, the greater the impact of coherence on the imaging quality, resulting in poorer imaging performance.

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Fusion of fractional vortex pairs and their transition to integer vortex controlled by optical power Chunzhi Sun(孙春志), Xiangwei Chen(陈向炜), Huizhong Xu, and Guo Liang(梁果) Chin. Phys. B, 2025, 34 (5):  054202.  DOI: 10.1088/1674-1056/adb8b9 Abstract ( 154 )   HTML ( 0 )   PDF (5220KB) ( 6 )   The evolution of fractional vortex pairs in free space and nonlocal nonlinear media is studied. In free space, the off-axis fractional vortex pairs of the-same-sign topological charge (TC) will be merged to one integer vortex at the beam center, which is drastically different from the dynamics of integer vortex pairs. In nonlocal nonlinear media, the conversion between the fractional vortex pair and the conventional integer vortex can be readily achieved by only tuning the input optical power. Therefore our approach provides a convenient way to control the number of vortices and thus the number of optical tweezers by adjusting the input optical power. These results may find potential applications in optical manipulation of particles.

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Enhancement of four-wave mixing due to coherent hole burning in a degenerate two-level system Zhi-Yuan Liu(刘知远), Yi-Fan Yao(姚一凡), Yue Sun(孙悦), Jia-Yu Han(韩佳瑜), and Ying-Jie Du(杜英杰) Chin. Phys. B, 2025, 34 (5):  054203.  DOI: 10.1088/1674-1056/adb949 Abstract ( 151 )   HTML ( 0 )   PDF (1121KB) ( 49 )   We present a theoretical study of four-wave mixing (FWM) in a degenerate two-level atomic system subject to a magnetic field whose Zeeman sublevels constitute a tripod-type atomic system, which is driven by a linearly polarized field, and coupled and probed by two sets of left and right circularly polarized fields. The optical effects of coherent hole burning (CHB) and electromagnetically induced transparency (EIT) are involved in the coherent system, among which the CHB has much larger response for the FWM than the EITs. Three situations of CHB are involved, and they are the solitary CHB, overlapped CHBs, and an overlap between CHB and EIT. The overlapped CHBs have the greatest magnitude of FWM signal among the three situations. Whereas, for the overlapped CHB and EIT, it has the smallest FWM magnitude, which is no more than one tenth of the former. While for the single CHB, the FWM magnitude is half of that of the overlapped CHBs. It is noted that, in the overlap between CHB and EIT, dual EIAs can be obtained, whose FWM signal also has an enhancement in comparison to no EIA.

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Precision flatness measurement based on orbital angular momentum Feifei Han(韩菲菲), Zhiwan Wang(王志琬), Le Wang(王乐), and Shengmei Zhao(赵生妹) Chin. Phys. B, 2025, 34 (5):  054204.  DOI: 10.1088/1674-1056/adbd14 Abstract ( 137 )   HTML ( 0 )   PDF (1922KB) ( 11 )   We propose a method to measure the flatness of an object with a petal-like pattern generated by the interference of the measured orbital angular momentum (OAM) beam and the reference OAM beam which carries the opposite OAM state. By calculating the difference between the petal rotation angle without/with the object, the thickness information of the object, and then the flatness information, can be evaluated. Furthermore, the direction of the object's flatness can be determined by the petal's clockwise/counterclockwise rotation. We theoretically analyze the relationship between the object's thickness and petal rotation angle, and verify the proposed method by experiment. The experimental results show that the proposed method is a high precision flatness measurement and can obtain the convex/concave property of the flatness. For the 1.02 mm glass sample, the mean deviation of the flatness is 1.357$\times {10}^{-8}$ and the variance is 0.242$\times {10}^{-16}$. For the 0.50 mm glass sample, the mean deviation of the flatness is 1.931$\times {10}^{-8}$ and the variance is 2.405$\times {10}^{-16}$. Two different topological charges are adopted for the 2.00 mm glass sample, and their flatness deviations are 0.239$\times {10}^{-8}$ ($\ell =1$) and 0.246$\times {10}^{-8}$ ($\ell =2$), where their variances are 0.799$\times {10}^{-18}$ ($\ell =1$) and 0.775$\times {10}^{-18}$ ($\ell =2$), respectively. It is shown that the flatness measured by the proposed method is the same for the same sample when different topological charges are used. All results indicate that the proposed method may provide a high flatness measurement, and will be a promising way to measure the flatness.

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Nonlinear Raman-Nath diffraction of inclined femtosecond laser by periodically poled lithium niobate nonlinear grating Jiacheng Li(李嘉诚), Lihong Hong(洪丽红), Yu Zou(邹娱), Jianluo Chen(陈健洛), and Zhi-Yuan Li(李志远) Chin. Phys. B, 2025, 34 (5):  054205.  DOI: 10.1088/1674-1056/adb67f Abstract ( 114 )   HTML ( 0 )   PDF (695KB) ( 6 )   When a pump laser beam strikes the surface of a nonlinear crystal with modulated second-order nonlinearity, various nonlinear diffraction phenomena occur, with nonlinear Raman-Nath diffraction (NRND) being a prominent example. In this study, we use an 800-nm Ti:sapphire femtosecond laser beam to pump the surface of a periodically poled lithium niobate (PPLN) crystal thin-plate nonlinear grating. By rotating the crystal, we change the incidence angle and observe and measure the exit angle, polarization, and power of NRND spots on the other side of the crystal. The experiment shows that NRND characteristics are highly sensitive to the incidence angle of the pump laser beam, which are consistent with the theoretical prediction. We expect that this research will advance the understanding of nonlinear diffraction and provide valuable insights for nonlinear optical interaction in complicated geometric and physical configurations.

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Experimental demonstration of silicon nitride waveguide gratings with excellent efficiency and divergence angle Zhaozhen Chen(陈兆震), Wenling Li(李文玲), Qian Wang(王乾), Enfeng Liu(刘恩峰), Xinqun Zhang(张新群), Jingwei Liu(刘敬伟), and Zhengsheng Han(韩郑生) Chin. Phys. B, 2025, 34 (5):  054206.  DOI: 10.1088/1674-1056/adbbbf Abstract ( 102 )   HTML ( 0 )   PDF (1671KB) ( 6 )   Silicon nitride (Si${}_3$N${}_4$) photonic platform has recently attracted increasing attention for Si${}_3$N${}_4$ photonic integrated circuits $(\mathrm{P}\mathrm{I}\mathrm{C})$. A diffraction grating with the only etched top-layer in tri-layer Si${}_3$N${}_4$ optical waveguides is proposed, which shows a simple fabrication process, high upward diffraction efficiency, and lower far-field divergence angle. The measured results of the diffraction grating at a wavelength of 905 nm show the average upward diffraction efficiency of 90.5% and average far-field divergence angle of 0.154${}^{\circ }$, which shows a good agreement with the design results with the upward diffraction efficiency of 91.6% and far-field divergence angle of 0.105${}^{\circ }$.

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Guiding and magneto-optical properties of TGG waveguide by proton implantation combined with femtosecond laser ablation Chun-Xiao Liu(刘春晓), Zi-Hao Wang(王子昊), Bei-Er Guo(郭贝尔), Rui Yuan(袁睿), Yi-Fan Wang(王逸凡), Yu-Hang Zhou(周雨航), Jia-Bin Sun(孙家彬), Liao-Lin Zhang(张料林), and Hai-Tao Guo(郭海涛) Chin. Phys. B, 2025, 34 (5):  054207.  DOI: 10.1088/1674-1056/adb9cc Abstract ( 123 )   HTML ( 0 )   PDF (851KB) ( 12 )   Integrating the magneto-optical effect into a waveguide-based photonic device becomes more and more interesting. In the work, the planar optical waveguide firstly was prepared in a terbium gallium garnet crystal (TGG) via the proton implantation with the energy of 4$\times {10}^{-1}$ MeV and the fluence of 6$\times {10}^8$ ions/μm${}^2$. Subsequently, a femtosecond laser with a central wavelength of 800 nm and a power of 3 mW was used to ablate the surface of the planar waveguide, forming the ridge optical waveguide. The dark-mode curve of the planar waveguide was measured by a prism coupling technique. The top-view morphology of the ridge waveguide was observed via a Nikon microscope. The mode field distributions of the planar and ridge waveguides were obtained by an end-face coupling system, and the propagation losses of the two waveguides were measured to be 2.26 dB/cm and 2.58 dB/cm, respectively. The Verdet constants were measured to be $-{72.7}^{\circ }$/T$\cdot$cm for the TGG substrate and $-{60.7}^{\circ }$/T$\cdot$cm for the ridge waveguide. The TGG waveguides have a potential in the fabrication of magneto-optical waveguide devices.

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Sobolev space norm regularized full waveform inversion for ultrasound computed tomography Panpan Li(李盼盼), Yubing Li(李玉冰), Chang Su(苏畅), Zeyuan Dong(董则元), and Weijun Lin(林伟军) Chin. Phys. B, 2025, 34 (5):  054301.  DOI: 10.1088/1674-1056/adbbc0 Abstract ( 134 )   HTML ( 0 )   PDF (7652KB) ( 33 )   Full waveform inversion (FWI) is a complex data fitting process based on full wavefield modeling, aiming to quantitatively reconstruct unknown model parameters from partial waveform data with high-resolution. However, this process is highly nonlinear and ill-posed, therefore achieving high-resolution imaging of complex biological tissues within a limited number of iterations remains challenging. We propose a multiscale frequency-domain full waveform inversion (FDFWI) framework for ultrasound computed tomography (USCT) imaging of biological tissues, which innovatively incorporates Sobolev space norm regularization for enhancement of prior information. Specifically, we investigate the effect of different types of hyperparameter on the imaging quality, during which the regularization weight is dynamically adapted based on the ratio of the regularization term to the data fidelity term. This strategy reduces reliance on predefined hyperparameters, ensuring robust inversion performance. The inversion results from both numerical and experimental tests (i.e., numerical breast, thigh, and ex vivo pork-belly tissue) demonstrate the effectiveness of our regularized FWI strategy. These findings will contribute to the application of the FWI technique in quantitative imaging based on USCT and make USCT possible to be another high-resolution imaging method after x-ray computed tomography and magnetic resonance imaging.

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Effect of metal plate on ultrasonic cavitation field distribution Jin-He Liu(刘金河), Zhuang-Zhi Shen(沈壮志), Peng-Fei Cao(曹鹏飞), Jian-Feng Li(李建锋), and Xiao-Qiang Bai(白小强) Chin. Phys. B, 2025, 34 (5):  054302.  DOI: 10.1088/1674-1056/adca9d Abstract ( 122 )   HTML ( 0 )   PDF (1087KB) ( 27 )   In order to enhance the ultrasonic degradation rate of organic solutions, a metal plate is placed at the water-air interface of the ultrasonic cleaning tank. Initially, the distribution of the acoustic field in the ultrasonic water tank was calculated using the simulation software COMSOL. The simulation results demonstrated that the utilization of the metal plate can eliminate the standing-wave acoustic field to a certain extent. Subsequently, the pixel method was selected for a quantitative comparison of the cavitation area in the flume with and without the metal plate. The results demonstrated that, under specific conditions, the area of ultrasonic cavitation in the water tank can be expanded using a metal plate. Thereafter, an acoustic degradation experiment was designed to confirm the feasibility of the simulation method. Furthermore, the impacts of the amplitude of the incident ultrasonic pressure, frequency, and the height of the liquid level in the water tank on the cavitation area were investigated.

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Finite element analysis of the impact of graphene filler dispersion on local hotspots in HMX-based PBX explosives Xuanyi Yang(杨烜屹), Xin Huang(黄鑫), Chaoyang Zhang(张朝阳), Yanqing Wang(王延青), and Yuxiang Ni(倪宇翔) Chin. Phys. B, 2025, 34 (5):  054401.  DOI: 10.1088/1674-1056/adb9ca Abstract ( 150 )   HTML ( 1 )   PDF (1167KB) ( 22 )   The incorporation of graphene fillers into polymer matrices has been recognized for its potential to enhance thermal conductivity, which is particularly beneficial for applications in thermal management. The uniformity of graphene dispersion is pivotal to achieving optimal thermal conductivity, thereby directly influencing the effectiveness of thermal management, including the mitigation of local hot-spot temperatures. This research employs a quantitative approach to assess the distribution of graphene fillers within a PBX (plastic-bonded explosive) matrix, focusing specifically on the thermal management of hot spots. Through finite element method (FEM) simulations, we have explored the impact of graphene filler orientation, proximity to the central heat source, and spatial clustering on heat transfer. Our findings indicate that the strategic distribution of graphene fillers can create efficient thermal conduction channels, which significantly reduce the temperatures at local hot spots. In a model containing 0.336% graphene by volume, the central hot-spot temperature was reduced by approximately 60 K compared to a pure PBX material, under a heat flux of 600 W/m${}^2$. This study offers valuable insights into the optimization of the spatial arrangement of low-concentration graphene fillers, aiming to improve the thermal management capabilities of HMX-based PBX explosives.

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Experimental study on the regulation of radiative heat flux by coating SiC film Haifeng Xia(閤海峰) and Huihui Sun(孙慧慧) Chin. Phys. B, 2025, 34 (5):  054402.  DOI: 10.1088/1674-1056/adbee0 Abstract ( 110 )   HTML ( 0 )   PDF (1755KB) ( 36 )   Near-field thermal radiation has received increased attention due to the performance of efficient energy conversion. In this study, the vacuum gap distance between two objects, separated by 1 μm polystyrene particles, is investigated. The entire experimental device is installed in a highly vacuumed environment to ensure that the radiative heat flux dominates the main mode of heat transfer. Compared with the measurement of near-field thermal radiation of flat glasses, it is found that coating SiC film on the hot side of optical glass can reduce heat transfer. However, through theoretical analysis, it is shown that there is an optimal thickness of SiC film of around 1 μm. In addition, the experimental data and theoretical analysis results are consistent. The experiment demonstrates that the regulation of radiative heat flux can be achieved by coating. As the thickness of SiC film on the hot side increases, the radiative heat flux decreases.

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Vibration modes of a bubble close to a boundary Jin-Ze Liu(刘金泽) and Wen-Shan Duan(段文山) Chin. Phys. B, 2025, 34 (5):  054701.  DOI: 10.1088/1674-1056/adbd24 Abstract ( 126 )   HTML ( 0 )   PDF (1392KB) ( 11 )   Using the recently proposed bubble equation, we study the vibration characteristics of a bubble close to a solid boundary. The results indicate that a rigid boundary has an important effect on large-amplitude bubble vibration. Whether the bubble vibration is stable or unstable strongly depends on the distance between the initial bubble center and the solid boundary. Furthermore, it also depends on both the amplitude and the frequency of the external perturbation. It is found that the smaller the distance between the initial bubble center and the solid boundary, the larger the initial bubble radius and the larger both the amplitude and frequency of the external perturbation, the more easily the bubble vibration becomes unstable. It is shown that this unstable bubble vibration is possibly related to the production of a reentrant microjet for the bubble, which suggests a potential method for estimating bubble size and the distance between the bubble center and the solid boundary by exerting an external perturbation with controllable amplitude and frequency on the liquid. Furthermore, the dependence of the natural frequency of the bubble on the external pressure for small-amplitude vibration can reveal the bubble radius and the distance between the bubble center and the solid boundary. In addition, the vibration characteristics of a bubble close to a solid boundary under a periodic external perturbation are revealed. Several bubble vibration modes are identified; the strongest vibration modes are those with the natural frequency and the external vibration frequency.

CONDENSED MATTER: STRUCTURAL, MECHANICAL, AND THERMAL PROPERTIES

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Enhanced electronic and photoelectrical properties of two-dimensional Zn-doped SnS2 Xichen Chuai(揣喜臣), Peng Yin(殷鹏), Jiawei Wang(王嘉玮), Guanhua Yang(杨冠华), Congyan Lu(陆丛研), Di Geng(耿玓), Ling Li(李泠), Can Liu(刘灿), Zhongming Wei(魏钟鸣), and Nianduan Lu(卢年端) Chin. Phys. B, 2025, 34 (5):  056101.  DOI: 10.1088/1674-1056/adbaca Abstract ( 126 )   HTML ( 0 )   PDF (1617KB) ( 29 )   Alloy engineering, with its ability to tune the electronic band structure, is regarded as an effective method for adjusting the electronic and optoelectronic properties of two-dimensional (2D) semiconductors. However, synthesizing metal-site substitution alloys remains challenging due to the low reactivity of metal precursors and the tendency for spatial phase separation during high-temperature growth. Here, we report the preparation of a high-quality metal-site substitution alloy, Zn${}_{0.167}$Sn${}_{0.833}$S${}_2$, via the chemical vapor transport method, which exhibits excellent photoresponsivity and enhanced electrical transport properties. Comprehensive characterization techniques, including Raman spectroscopy, x-ray photoelectron spectroscopy (XPS), and electron microscopy, unambiguously confirm the uniform Zn substitution in the as-prepared Zn${}_{0.167}$Sn${}_{0.833}$S${}_2$ alloy. Furthermore, the photodetector based on the Zn${}_{0.167}$Sn${}_{0.833}$S${}_2$ alloy demonstrated a high on/off ratio of 51 under white light, a wide spectral response range from 350 nm to 900 nm, and a broad dynamic power range of 80 dB under 638-nm illumination. In terms of transport properties, field-effect transistors (FETs) based on Zn${}_{0.167}$Sn${}_{0.833}$S${}_2$ achieved a carrier mobility of 6.5 cm${}^2\cdot$V${}^{-1}\cdot$s${}^{-1}$, which is six times higher than that of SnS${}_2$. This alloy semiconductor showcases significantly enhanced electronic and optoelectronic properties, offering great potential for the development of high-resolution photodetection technologies.

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Ultrahigh concentration of NV- centers embedded in the CVD epi-diamond layer near the interface with an HPHT diamond substrate Yuanjie Yang(杨元杰), Shengran Lin(林盛然), Jiaxin Zhao(赵嘉昕), Changfeng Weng(翁长风), Liren Lou(楼立人), Wei Zhu(祝巍), and Guanzhong Wang(王冠中) Chin. Phys. B, 2025, 34 (5):  056102.  DOI: 10.1088/1674-1056/adc7f5 Abstract ( 120 )   HTML ( 0 )   PDF (1014KB) ( 11 )   The negatively charged nitrogen vacancy (NV${}^{-}$) center ensemble in as-grown chemical vapor deposition (CVD) diamond is a promising candidate for quantum sensing due to its long coherence time and excellent optical properties. However, achieving a high concentration of NV${}^{-}$ centers in as-grown CVD diamond remains a critical challenge, which constrains the performance of NV${}^{-}$ based sensors. In this study, we observe that NV${}^{-}$ center formation efficiency is significantly enhanced during the initial growth phase, with a coherence time $T_2^{\ast }$ of 1.1 μs. These findings demonstrate that high-concentration NV${}^{-}$ centers can be achieved in as-grown diamonds, greatly enhancing their utility in high-performance magnetometers and quantum sensing.

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Modeling of microstructure and microsegregation evolution in solidification of ternary alloys Qiannan Yu(于芊楠), Mengdan Hu(胡梦丹), Jinyi Wu(吴津仪), and Dongke Sun(孙东科) Chin. Phys. B, 2025, 34 (5):  056801.  DOI: 10.1088/1674-1056/adb8b5 Abstract ( 110 )   HTML ( 0 )   PDF (3373KB) ( 7 )   The microstructure formed during solidification has a significant impact on the mechanical properties of materials. In this study, a two-dimensional (2D) cellular automaton (CA)-finite difference (FD)-CALPHAD model was developed to simulate the formation of microstructure and solute segregation in the solidification processes of ternary alloys. In the model, dendritic growth is simulated using the CA technique, while solute diffusion is solved by the FD method, and the CALPHAD method is employed to calculate thermodynamic phase equilibrium during solidification. The CA-FD-CALPHAD coupled model is capable of reproducing the evolution of continuous nucleation and growth of grains as well as the evolution of the microstructure and solute distribution during solidification of ternary alloys. In this study, Al-Zn-Mg ternary alloy is taken as an example to simulate the growth of equiaxed and columnar grains and the columnar-to-equiaxed transition (CET) under different solidification conditions. The simulation results are compared with experimental data from the literature, showing a good agreement. Besides, the study also investigates the evolution of temperature and multicomponent solute fields during solidification and the effects of alloy composition and cooling rate on the microstructure morphology. The results reveal that the initial alloy composition and cooling rate significantly affect dendritic morphology and solute segregation. Higher initial alloy concentrations promote the growth of side branches in equiaxed grains, leading to more pronounced solute segregation between dendrites. As the cooling rate increases, the average grain size of the equiaxed grains decreases accordingly. Additionally, a higher cooling rate accelerates the columnar-to-equiaxed transition, leading to a finer grain structure.

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Surface solitonic charge distribution on 2D materials investigated using Kelvin probe force microscopy technique based on qplus atomic force microscopy Rui Song(宋睿), Feng Hao(郝峰), Jie Yang(杨杰), Lifeng Yin(殷立峰), and Jian Shen(沈健) Chin. Phys. B, 2025, 34 (5):  056802.  DOI: 10.1088/1674-1056/adbee8 Abstract ( 145 )   HTML ( 0 )   PDF (2616KB) ( 17 )   Recently, charged solitons have been found in a two-dimensional CoCl${}_2$/HOPG system, whose microscopic nature remains to be elusive. In this work, we investigate the charged solitons in monolayer CoCl${}_2$ using scanning tunneling microscopy (STM) and atomic force microscopy (AFM). Moreover, we study the electrical properties of the charged solitons at zero electric field by measuring local contact potential difference (LCPD) via Kelvin probe force microscopy (KPFM) using the $\mathrm{\Delta }f(V)$ method. The compensation voltage corresponding to the vertex of the parabola is obtained by fitting the quadratic relationship between $\mathrm{\Delta }f$ and sample bias. The results show that, without an external electric field, the solitons behave as negatively charged entities. Meanwhile, the LCPD mapping characterizes the spatial distribution of the potential at the charged solitons, which agrees well with those obtained from STM band bending measurements.

CONDENSED MATTER: ELECTRONIC STRUCTURE, ELECTRICAL, MAGNETIC, AND OPTICAL PROPERTIES

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Relativistic non-Fermi liquid fixed point in (2+1)-dimensional birefringent Dirac fermions interacting with electromagnetic fields Wan-Zi Sun(孙万梓), Kai Liu(刘恺), Wu-Ming Liu(刘伍明), and Cheng-Xi Li(李成蹊) Chin. Phys. B, 2025, 34 (5):  057102.  DOI: 10.1088/1674-1056/adb9cd Abstract ( 125 )   HTML ( 0 )   PDF (911KB) ( 33 )   The system consisting of (2+1)-dimensional quasirelativistic birefringent Dirac fermions with Coulomb interactions and retarded current-current interactions is described by a quantum field theory similar to reduced quantum electrodynamics. We used the perturbative renormalization group method to study the low-energy behavior of the system and found that it flows to a fixed point of the non-Fermi liquid composed of relativistic pseudospin-1/2 Dirac fermions in the deep infrared limit. At the fixed point, the fermion Green function exhibits a finite anomalous dimension, and the residue of the quasiparticle pole vanishes in a power-law fashion. Our research provides new theoretical perspectives for understanding the origin of spin-1/2 fermions in the standard model.

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Predicted stable two-dimensional semiconductor TiOS materials with promising photocatalytic properties: First-principles calculations Pan Zhang(张攀), Shihai Fu(付世海), Chunying Pu(濮春英), Xin Tang(唐鑫), and Dawei Zhou(周大伟) Chin. Phys. B, 2025, 34 (5):  057103.  DOI: 10.1088/1674-1056/adb687 Abstract ( 159 )   HTML ( 1 )   PDF (3003KB) ( 41 )   TiO${}_2$ is a well-known photocatalyst with a band gap of 3.2 eV, yet its ability to absorb light is limited to the short wavelengths of ultraviolet light. To achieve a more effective photocatalytic material, we have designed two-dimensional semiconductor TiOS materials using swarm intelligence algorithms combined with first-principles calculations. Three stable low-energy structures with space groups of $P$2${}_1/m$, $P$3$m$1 and $P$2${}_1/c$ are identified. Among these structures, the Janus $P$3$m$1 phase is a direct bandgap semiconductor, while the $P$2${}_1/m$ and $P$2${}_1/c$ phases are indirect bandgap semiconductors. Utilizing the accurate hybrid density functional HSE06 method, the band gaps of the three structures are calculated to be 2.34 eV ($P$2${}_1/m$), 2.24 eV ($P$3$m$1) and 3.22 eV ($P$2${}_1/c)$. Optical calculations reveal that TiOS materials exhibit a good light-harvesting capability in both visible and ultraviolet spectral ranges. Moreover, the photocatalytic calculations also indicate that both $P$2${}_1/m$ and $P$3$m$1 TiOS can provide a strong driving force for converting H${}_2$O to H${}_2$ and O${}_2$ in an acidic environment with pH $=$ 0. The structural stabilities, mechanical properties, electronic structures and hydrogen evolution reaction activities are also discussed in detail. Our research suggests that two-dimensional TiOS materials have potential applications in both semiconductor devices and photocatalysis.

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Amorphous IGMO/IGZO heterojunction thin-film transistors with enhanced ultraviolet detection performance Jichun Yao(姚继春), Yiyu Zhang(张怡宇), and Xingzhao Liu(刘兴钊) Chin. Phys. B, 2025, 34 (5):  057104.  DOI: 10.1088/1674-1056/adb8b6 Abstract ( 136 )   HTML ( 0 )   PDF (870KB) ( 40 )   Amorphous InGaZnO (IGZO) is a potential candidate for integrated circuits based on thin-film transistors (TFTs) owing to its low-temperature processability and high mobility. Amorphous InGaMgO/InGaZnO (IGMO/IGZO) heterojunction was deposited and TFTs based on IGMO/IGZO heterojunction were fabricated in this report. The energy band at the IGMO/IGZO heterojunction was characterized, and the potential well at the interface of IGZO is critical to the enhanced ultraviolet detection of the IGMO/IGZO heterojunction. Furthermore, the TFTs based on IGMO/IGZO heterojunction exhibited a high responsivity of 3.8$\times {10}^3$ A/W and a large detectivity of 5.2$\times {10}^{14}$ Jones under 350-nm ultraviolet illumination, which will also benefit for fabrication of monolithic ultraviolet sensing chip.

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Enhanced thermoelectric properties of the topological phase of monolayer HfC Wenlai Mu(母文来), Nisar Muhammad(穆罕默德·尼萨), Baojuan Dong(董宝娟), Nguyen Tuan Hung(阮俊兴), Huaihong Guo(郭怀红), Riichiro Saito(斋藤理一郎), Weijiang Gong(公卫江), Teng Yang(杨腾), and Zhidong Zhang(张志东) Chin. Phys. B, 2025, 34 (5):  057301.  DOI: 10.1088/1674-1056/adbd17 Abstract ( 120 )   HTML ( 0 )   PDF (6215KB) ( 28 )   Thermoelectric properties of a topological insulator, monolayer HfC, are calculated using first-principles calculation, which accounts for the two contributions from edge and bulk states. By applying strain up to 8% along the $a$ axis, the monolayer HfC shows the topological phase while it is in a non-topological state without strain. The figure of merit, $ZT$, for the topological phase becomes two-ordered magnitude larger ($ZT$ $\sim$ 2) because of larger electric conductivity than that of the non-topological phase due to edge current. The total Seebeck coefficient $S$, and $ZT$ have maximum values when the chemical potential is located at the highest energy of the edge state. The peak of $ZT$ comes from the fact that the product of divergent $S$ and quickly-decreasing electric conductivity above the highest energy of the edge state. We further optimize $S$ and $ZT$ by changing the sample size and temperature.

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Anisotropic two-band α-model and its application to layered chalcogenide superconductor NbSe2 Jiang-Ning Zhang(张江宁), Guo Wang(王果), Tian-Yi Han(韩天意), and Hai Huang(黄海) Chin. Phys. B, 2025, 34 (5):  057401.  DOI: 10.1088/1674-1056/adbbbe Abstract ( 143 )   HTML ( 0 )   PDF (769KB) ( 18 )   The generalized $\alpha$-model for anisotropic two-band superconductivity is consistently constructed with the consideration of weak interband electron-electron interaction. Tailored from the two-band BCS theory, the developed framework can be applied to investigate thermodynamic properties of intraband strong-coupling superconductors. Accordingly, we perform a calculation on the temperature dependence of specific heat and obtain an analytic expression for specific heat jump at the superconducting critical temperature. Meanwhile, we also compute the superfluid density and the spin susceptibility with this formalism. Given the low-temperature superconducting gaps from experimental measurement, all of our theoretical results can fit the experimental data of the layered two-band superconductor NbSe${}_2$ well.

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Effective strategy of enhancing piezoelectricity in stable CrSiN4Sn semiconductor monolayers by atom-layer-pair effect Qi-Wen He(贺绮雯), Dan-Yang Zhu(朱丹阳), Jun-Hui Wang(王俊辉), He-Na Zhang(张贺娜), Xiao Shang(尚骁), Shou-Xin Cui(崔守鑫), and Xiao-Chun Wang(王晓春) Chin. Phys. B, 2025, 34 (5):  057701.  DOI: 10.1088/1674-1056/adb7d1 Abstract ( 148 )   HTML ( 0 )   PDF (4850KB) ( 4 )   It is challenging to reveal the design strategy for strong piezoelectricity nano-materials used in self-powered and smart nano-devices. Through first-principles calculations, an atom-layer-pair effect is found in MoSi${}_x$N${}_y{R}_z$ monolayers with remarkable piezoelectricity. The absolute values of the vertical piezoelectric coefficients have a linear relation with the total electronegativity difference dipole moments. Based on this effect, a promising CrSiN${}_4$Sn monolayer is found with the highest piezoelectricity among the above monolayers. The work expands our understanding of the piezoelectric physical mechanism and provides the design strategy for piezoelectric nano-devices.

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Effects of helium ion irradiation and thermal annealing on the optical and structural properties of hexagonal boron nitride Guan-Lin Liu(刘冠麟), Ji-Lian Xu(徐辑廉), Peng-Tao Jing(景鹏涛), Jing-Jing Shao(邵京京), Xu Guo(郭旭), Yun-Tao Wu(吴韵涛), Feng Qin(覃凤), Zhen Cheng(程祯), Deming Liu(刘德明), Yang Bao(鲍洋), Hai Xu(徐海), Li-Gong Zhang(张立功), Da Zhan(詹达), Jia-Xu Yan(闫家旭), Lei Liu(刘雷), and De-Zhen Shen(申德振) Chin. Phys. B, 2025, 34 (5):  057801.  DOI: 10.1088/1674-1056/adbee7 Abstract ( 179 )   HTML ( 0 )   PDF (3435KB) ( 29 )   Hexagonal boron nitride (h-BN) has emerged as a promising two-dimensional material for quantum and optoelectronic applications, with its unique ability to host engineered defects enabling single-photon emission and spin manipulation. This study investigates defect formation in h-BN using focused helium ion beam (He${}^{+}$ FIB) irradiation and post-annealing treatments. We demonstrate that helium ion irradiation at doses up to $2\times {10}^9$ ions/μm${}^2$ does not induce phase transitions or amorphization. Spectroscopic analyses, including differential reflectance spectroscopy (DRS), photoluminescence (PL), and Raman spectroscopy, reveal substantial defect formation and structural modifications. Notably, the irradiation induces a softening of in-plane and interlayer phonon modes, characterized by frequency redshifts of 10.5 cm${}^{-1}$ and 3.2 cm${}^{-1}$, respectively. While high-temperature thermal annealing mitigates lattice defects and facilitates single-photon emission, the E${}_{2\mathrm{g}}$ peak width remains 38% broader and the shear mode peak width is 60% broader compared to pre-annealing conditions in the Raman spectra, indicating residual structural degradation. These findings provide insights into defect engineering mechanisms in h-BN, offering guidance for optimizing processing conditions and advancing quantum and optoelectronic device technologies.

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Stokes/anti-Stokes Raman spectroscopy of Al0.86Ga0.14N semiconductor alloy Yuru Lin(林玉茹), Yu Li(李宇), Binbin Wu(吴彬彬), Jingyi Liu(刘静仪), Ruiang Guo(郭睿昂), Yangbin Wang(王扬斌), Qiwei Hu(胡启威), and Li Lei(雷力) Chin. Phys. B, 2025, 34 (5):  057802.  DOI: 10.1088/1674-1056/adb67d Abstract ( 179 )   HTML ( 0 )   PDF (1519KB) ( 44 )   The lattice dynamics of a high Al composition semiconductor alloy, Al${}_{0.86}$Ga${}_{0.14}$N, in comparison with intrinsic GaN and AlN are studied by Stokes/anti-Stokes Raman spectroscopy in the temperature range of 85-823 K. The phonon anharmonic effect in Al${}_{0.86}$Ga${}_{0.14}$N is found to be stronger than that in GaN, revealing low thermal conductivity in the semiconductor alloy. Multi-phonon coupling behavior is analyzed by both Stokes Raman and anti-Stokes Raman spectroscopy. It is interesting to find that the anti-Stokes scattering exhibits stronger three-phonon coupling than the Stokes scattering, which may be due to the fact that the anti-stokes scattering process is generated from an excited state and the scattered photons have higher energies. The Stokes/anti-Stokes temperature correction factor $\beta$ for Raman modes in Al${}_{0.86}$Ga${}_{0.14}$N alloy are all smaller than those of the corresponding intrinsic modes in GaN and AlN. The reasons for the difference in $\beta$ can be attributed to three aspects, including the equipment setups, materials properties (the binding energy) and the coupling strength of Raman scattering and the sample.

INTERDISCIPLINARY PHYSICS AND RELATED AREAS OF SCIENCE AND TECHNOLOGY

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Synthesis of two-dimensional diamond by phase transition from graphene at atmospheric pressure Songyang Li(李松洋), Zhiguang Zhu(朱志光), Youzhi Zhang(张有志), Chengke Chen(陈成克), and Xiaojun Hu(胡晓君) Chin. Phys. B, 2025, 34 (5):  058101.  DOI: 10.1088/1674-1056/adb688 Abstract ( 117 )   HTML ( 0 )   PDF (5112KB) ( 10 )   It is a key challenge to prepare two-dimensional diamond (2D-diamond). Herein, we develop a method for synthesizing 2D-diamond by depositing monodisperse tantalum (Ta) atoms onto graphene substrates using a hot-filament chemical vapor deposition setup, followed by annealing treatment under different temperatures at ambient pressure. The results indicate that when the annealing temperature increases from 700 ${}^{\circ }$C to 1000 ${}^{\circ }$C, the size of the 2D-diamond found in the samples gradually increases from close to 20 nm to around 30 nm. Meanwhile, the size and number of amorphous carbon spheres and Ta-containing compounds between the graphene layers gradually increase. As the annealing temperature continues to rise to 1100 ${}^{\circ }$C, a significant aggregation of Ta-containing compounds is observed in the samples, with no diamond structure detected. This further confirms that monodisperse Ta atoms play a key role in graphene phase transition into 2D-diamond. This study provides a novel method for the ambient-pressure phase transition of graphene into 2D-diamond.

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Protein aging dynamics: A perspective from non-equilibrium coarse-grained models Yue Shan(单月), Chun-Lai Ren(任春来), and Yu-Qiang Ma(马余强) Chin. Phys. B, 2025, 34 (5):  058301.  DOI: 10.1088/1674-1056/adbd16 Abstract ( 135 )   HTML ( 1 )   PDF (1972KB) ( 27 )   The aging of biomolecular condensates has been implicated in the pathogenesis of various neurodegenerative diseases, characterized by a transition from a physiologically liquid-like state to a pathologically ordered structure. However, the mechanisms governing the formation of these pathological aggregates remain poorly understood. To address this, the present study utilizes coarse-grained molecular dynamics simulations based on Langevin dynamics to explore the structural, dynamical, and material property changes of protein condensates during the aging process. Here, we further develop a non-equilibrium simulation algorithm that not only captures the characteristics of time-dependent amount of aging beads but also reflects the structural information of chain-like connections between aging beads. Our findings reveal that aging induces compaction of the condensates, accompanied by a decrease in diffusion rates and an increase in viscosity. Further analysis suggests that the heterogeneous diffusivity within the condensates may drive the aging process to initiate preferentially at the condensate surface. Our simulation results align with the experimental phenomena and provide a clear physical picture of the aging dynamics.

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Effects of palmitoylation on membrane protein partitioning into lipid domains in model cellular membranes Shishi Wu(吴施施) and Qing Liang(梁清) Chin. Phys. B, 2025, 34 (5):  058701.  DOI: 10.1088/1674-1056/adbee9 Abstract ( 97 )   HTML ( 2 )   PDF (1412KB) ( 45 )   The partitioning of membrane proteins into lipid domains in cellular membranes is closely associated with the realization of the protein functions and it is influenced by various factors such as the post-translational modification of palmitoylation. However, the molecular mechanism of the effect of palmitoylation on membrane protein partitioning into the lipid domains remains elusive. In this work, taking human peripheral myelin protein 22 (PMP22) as an example, we employ coarse-grained molecular dynamics simulations to investigate the partitioning of both the natural PMP22 and the palmitoylated PMP22 (pal-PMP22) into the lipid domains of model myelin membranes. The results indicate that palmitoylation drives PMP22 to localize at the boundary of the liquid-ordered (Lo) and liquid-disordered (Ld) domains and increases the possibility of PMP22 partitioning into the Lo domains by changing the hydrophobic length of the proteins and perturbing the ordered packing of tails of the saturated lipids in the Lo domains. This work offers some novel insights into the role of palmitoylation in modulating the function of membrane proteins in cellular membranes.

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Tunable working bandwidth terahertz switch based on magnetic valley photonic crystal Mingxia Hou(侯铭霞), Hongming Fei(费宏明), Han Lin(林瀚), and Mingda Zhang(张明达) Chin. Phys. B, 2025, 34 (5):  058702.  DOI: 10.1088/1674-1056/adbb5b Abstract ( 97 )   HTML ( 0 )   PDF (1951KB) ( 42 )   Terahertz (THz) switches are essential components of THz communication systems. THz switches based on conventional waveguides and photonic crystal structures are sensitive to manufacturing defects and sharp bending, resulting in high scattering losses. In addition, THz switches with tunable working bandwidths have not yet been demonstrated. Here, we design THz switches based on a topological valley photonic crystal (VPC) structure using magnetic materials, which can achieve high forward transmittance based on the unique spin-valley locking effect. The broad working bandwidth allows selective turning on and off at a designed wavelength region by controlling the applied magnetic field. The designed THz switch can achieve an extinction ratio of up to 31.66 dB with an insertion loss of less than 0.13 dB. The 3-dB bandwidth is up to 49 GHz. This tunable THz switch can be experimentally fabricated by current fabrication techniques and thus can find broad applications in THz communication systems.

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Irreversibility as a signature of non-equilibrium phase transition in large-scale human brain networks: An fMRI study Jing Wang(王菁), Kejian Wu(吴克俭), Jiaqi Dong(董家奇), and Lianchun Yu(俞连春) Chin. Phys. B, 2025, 34 (5):  058703.  DOI: 10.1088/1674-1056/adbd27 Abstract ( 135 )   HTML ( 1 )   PDF (1181KB) ( 43 )   It has been argued that the human brain, as an information-processing machine, operates near a phase transition point in a non-equilibrium state, where it violates detailed balance leading to entropy production. Thus, the assessment of irreversibility in brain networks can provide valuable insights into their non-equilibrium properties. In this study, we utilized an open-source whole-brain functional magnetic resonance imaging (fMRI) dataset from both resting and task states to evaluate the irreversibility of large-scale human brain networks. Our analysis revealed that the brain networks exhibited significant irreversibility, violating detailed balance, and generating entropy. Notably, both physical and cognitive tasks increased the extent of this violation compared to the resting state. Regardless of the state (rest or task), interactions between pairs of brain regions were the primary contributors to this irreversibility. Moreover, we observed that as global synchrony increased within brain networks, so did irreversibility. The first derivative of irreversibility with respect to synchronization peaked near the phase transition point, characterized by the moderate mean synchronization and maximized synchronization entropy of blood oxygenation level-dependent (BOLD) signals. These findings deepen our understanding of the non-equilibrium dynamics of large-scale brain networks, particularly in relation to their phase transition behaviors, and may have potential clinical applications for brain disorders.

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Exploring the proper statistical proxy to distinguish random structures Mei Xie(解梅), Fei Xie(谢飞), Baoyu Song(宋宝玉), Qiaoyu Guo(郭桥雨), and Xuechen Jiao(焦学琛) Chin. Phys. B, 2025, 34 (5):  058902.  DOI: 10.1088/1674-1056/adbd2b Abstract ( 104 )   HTML ( 0 )   PDF (1962KB) ( 12 )   The canonical description of structures comprises two aspects: (1) basic structural elements and (2) arrangement pattern between those elements. This tidy description has been very successful and facilitates the development of structural physics tremendously, enabling the classification, comparison and analysis of an extremely wide range of structures, including crystals, quasi-crystals, liquid crystals, semi-crystalline materials and so on. However, it has been gradually realized that many novel materials and devices exhibit random structures in which either basic elements or arrangement patterns may not exist. With the rapid development of modern advanced materials, this type of apparently random structure pops up frequently, leaving researchers struggling with how to describe, classify and quantitatively compare them. This paper proposes the utilization of statistical characteristics as the major indicators for the description of apparently random structures. Specifically, we have explored many statistical properties, including power spectral density, histograms, structural complexity, entropic complexity, autocorrelation, etc., and found that autocorrelation may serve as a promising statistical proxy to distinguish similar-looking random structures. We discuss eight atomic force microscope images of random structures, demonstrating that autocorrelation can be used to distinguish them. In addition, 14 more diverse datasets are used to support this conclusion, including atomic force microscopy images of polymers and non-polymers, transmission electron microscopy images of nanocomposite layers and scanning electron microscopy images of non-polymers.