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Chin. Phys. B, 2022, Vol. 31(12): 120502    DOI: 10.1088/1674-1056/ac7a0d
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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
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.
Keywords:  quantum chaos      dynamical localization      resonance and topology  
Received:  12 January 2022      Revised:  19 April 2022      Accepted manuscript online:  18 June 2022
PACS:  05.45.-a (Nonlinear dynamics and chaos)  
  05.45.Mt (Quantum chaos; semiclassical methods)  
Fund: 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).
Corresponding Authors:  Xiaoping Zhang, Zhongzhou Ren     E-mail:;

Cite this article: 

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 2022 Chin. Phys. B 31 120502

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