Resonance and antiresonance characteristics in linearly delayed Maryland model

doi:10.1088/1674-1056/ac7a0d

中国物理B ›› 2022, Vol. 31 ›› Issue (12): 120502-120502.doi: 10.1088/1674-1056/ac7a0d

Resonance and antiresonance characteristics in linearly delayed Maryland model

Hsinchen Yu(于心澄)^1,2,3, Dong Bai(柏栋)⁴, Peishan He(何佩珊)^1,2, Xiaoping Zhang(张小平)^1,2,†, Zhongzhou Ren(任中洲)^4,5,‡, and Qiang Zheng(郑强)⁶

1 State Key Laboratory of Lunar and Planetary Sciences, Macau University of Science and Technology, Macau 999078, China;
2 CNSA Macau Center for Space Exploration and Science, Macau, China;
3 Department of Physics, Nanjing University, Nanjing 210008, China;
4 School of Physics Science and Engineering, Tongji University, Shanghai 200092, China;
5 Key Laboratory of Advanced Micro-Structure Materials(MOE), Tongji University, Shanghai 200092, China;
6 School of Physical Science and Technology, Tiangong University, Tianjin 300387, China

收稿日期:2022-01-12 修回日期:2022-04-19 接受日期:2022-06-18 出版日期:2022-11-11 发布日期:2022-11-19
通讯作者: Xiaoping Zhang, Zhongzhou Ren E-mail:xpzhangnju@gmail.com;zren@tongji.edu.cn
基金资助:
Project supported by the Science and Technology Development Fund (FDCT) of Macau, China (Grant Nos. 0014/2022/A1 and 0042/2018/A2) and the National Natural Science Foundation of China (Grant Nos. 11761161001, 12035011, and 11975167).

Resonance and antiresonance characteristics in linearly delayed Maryland model

Hsinchen Yu(于心澄)^1,2,3, Dong Bai(柏栋)⁴, Peishan He(何佩珊)^1,2, Xiaoping Zhang(张小平)^1,2,†, Zhongzhou Ren(任中洲)^4,5,‡, and Qiang Zheng(郑强)⁶

1 State Key Laboratory of Lunar and Planetary Sciences, Macau University of Science and Technology, Macau 999078, China;
2 CNSA Macau Center for Space Exploration and Science, Macau, China;
3 Department of Physics, Nanjing University, Nanjing 210008, China;
4 School of Physics Science and Engineering, Tongji University, Shanghai 200092, China;
5 Key Laboratory of Advanced Micro-Structure Materials(MOE), Tongji University, Shanghai 200092, China;
6 School of Physical Science and Technology, Tiangong University, Tianjin 300387, China

Received:2022-01-12 Revised:2022-04-19 Accepted:2022-06-18 Online:2022-11-11 Published:2022-11-19
Contact: Xiaoping Zhang, Zhongzhou Ren E-mail:xpzhangnju@gmail.com;zren@tongji.edu.cn
Supported by:
Project supported by the Science and Technology Development Fund (FDCT) of Macau, China (Grant Nos. 0014/2022/A1 and 0042/2018/A2) and the National Natural Science Foundation of China (Grant Nos. 11761161001, 12035011, and 11975167).

摘要/Abstract

摘要： The Maryland model is a critical theoretical model in quantum chaos. This model describes the motion of a spin-1/2 particle on a one-dimensional lattice under the periodical disturbance of the external delta-function-like magnetic field. In this work, we propose the linearly delayed quantum relativistic Maryland model (LDQRMM) as a novel generalization of the original Maryland model and systematically study its physical properties. We derive the resonance and antiresonance conditions for the angular momentum spread. The "characteristic sum" is introduced in this paper as a new measure to quantify the sensitivity between the angular momentum spread and the model parameters. In addition, different topological patterns emerge in the LDQRMM. It predicts some additions to the Anderson localization in the corresponding tight-binding systems. Our theoretical results could be verified experimentally by studying cold atoms in optical lattices disturbed by a linearly delayed magnetic field.

关键词: quantum chaos, dynamical localization, resonance and topology

Abstract: The Maryland model is a critical theoretical model in quantum chaos. This model describes the motion of a spin-1/2 particle on a one-dimensional lattice under the periodical disturbance of the external delta-function-like magnetic field. In this work, we propose the linearly delayed quantum relativistic Maryland model (LDQRMM) as a novel generalization of the original Maryland model and systematically study its physical properties. We derive the resonance and antiresonance conditions for the angular momentum spread. The "characteristic sum" is introduced in this paper as a new measure to quantify the sensitivity between the angular momentum spread and the model parameters. In addition, different topological patterns emerge in the LDQRMM. It predicts some additions to the Anderson localization in the corresponding tight-binding systems. Our theoretical results could be verified experimentally by studying cold atoms in optical lattices disturbed by a linearly delayed magnetic field.

Key words: quantum chaos, dynamical localization, resonance and topology

中图分类号: (Nonlinear dynamics and chaos)

05.45.-a

05.45.Mt (Quantum chaos; semiclassical methods)

Hsinchen Yu(于心澄), Dong Bai(柏栋), Peishan He(何佩珊), Xiaoping Zhang(张小平), Zhongzhou Ren(任中洲), and Qiang Zheng(郑强). Resonance and antiresonance characteristics in linearly delayed Maryland model[J]. 中国物理B, 2022, 31(12): 120502-120502.

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Resonance and antiresonance characteristics in linearly delayed Maryland model

Resonance and antiresonance characteristics in linearly delayed Maryland model

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