Level spacing statistics for two-dimensional massless Dirac billiards

doi:10.1088/1674-1056/23/7/070507

中国物理B ›› 2014, Vol. 23 ›› Issue (7): 70507-070507.doi: 10.1088/1674-1056/23/7/070507

所属专题： TOPICAL REVIEW — Statistical Physics and Complex Systems

• TOPICAL REVIEW—Statistical Physics and Complex Systems • 上一篇下一篇

Level spacing statistics for two-dimensional massless Dirac billiards

黄亮^{a b}, 徐洪亚^{a b}, 来颖诚^{b c d}, Celso Grebogid^d

a Institute of Computational Physics and Complex Systems and Key Laboratory for Magnetism and Magnetic Materials of MOE, Lanzhou University, Lanzhou 730000, China;
b School of Electrical, Computer, and Energy Engineering, Arizona State University, Tempe, AZ 85287, USA;
c Department of Physics, Arizona State University, Tempe, AZ 85287, USA;
d Institute for Complex Systems and Mathematical Biology, School of Natural and Computing Sciences, King's College, University of Aberdeen, UK

收稿日期:2014-03-05 修回日期:2014-05-22 出版日期:2014-07-15 发布日期:2014-07-15
基金资助:
Project supported by the National Natural Science Foundation of China (Grant Nos. 11005053, 11135001, and 11375074), the Air Force Office of Scientific Research (Grant No. FA9550-12-1-0095), and the Office of Naval Research (Grant No. N00014-08-1-0627).

Level spacing statistics for two-dimensional massless Dirac billiards

Huang Liang (黄亮)^{a b}, Xu Hong-Ya (徐洪亚)^{a b}, Lai Ying-Cheng (来颖诚)^{b c d}, Celso Grebogi^d

a Institute of Computational Physics and Complex Systems and Key Laboratory for Magnetism and Magnetic Materials of MOE, Lanzhou University, Lanzhou 730000, China;
b School of Electrical, Computer, and Energy Engineering, Arizona State University, Tempe, AZ 85287, USA;
c Department of Physics, Arizona State University, Tempe, AZ 85287, USA;
d Institute for Complex Systems and Mathematical Biology, School of Natural and Computing Sciences, King's College, University of Aberdeen, UK

Received:2014-03-05 Revised:2014-05-22 Online:2014-07-15 Published:2014-07-15
Contact: Huang Liang E-mail:huangl@lzu.edu.cn
About author:05.45.Mt; 03.65.Pm; 73.22.Dj
Supported by:
Project supported by the National Natural Science Foundation of China (Grant Nos. 11005053, 11135001, and 11375074), the Air Force Office of Scientific Research (Grant No. FA9550-12-1-0095), and the Office of Naval Research (Grant No. N00014-08-1-0627).

摘要/Abstract

摘要： Classical-quantum correspondence has been an intriguing issue ever since quantum theory was proposed. The searching for signatures of classically nonintegrable dynamics in quantum systems comprises the interesting field of quantum chaos. In this short review, we shall go over recent efforts of extending the understanding of quantum chaos to relativistic cases. We shall focus on the level spacing statistics for two-dimensional massless Dirac billiards, i.e., particles confined in a closed region. We shall discuss the works for both the particle described by the massless Dirac equation (orWeyl equation) and the quasiparticle from graphene. Although the equations are the same, the boundary conditions are typically different, rendering distinct level spacing statistics.

关键词: quantum chaos, level spacing statistics, Dirac billiards, graphene billiards

Abstract: Classical-quantum correspondence has been an intriguing issue ever since quantum theory was proposed. The searching for signatures of classically nonintegrable dynamics in quantum systems comprises the interesting field of quantum chaos. In this short review, we shall go over recent efforts of extending the understanding of quantum chaos to relativistic cases. We shall focus on the level spacing statistics for two-dimensional massless Dirac billiards, i.e., particles confined in a closed region. We shall discuss the works for both the particle described by the massless Dirac equation (orWeyl equation) and the quasiparticle from graphene. Although the equations are the same, the boundary conditions are typically different, rendering distinct level spacing statistics.

Key words: quantum chaos, level spacing statistics, Dirac billiards, graphene billiards

中图分类号: (Quantum chaos; semiclassical methods)

05.45.Mt

03.65.Pm (Relativistic wave equations) 73.22.Dj (Single particle states)

黄亮, 徐洪亚, 来颖诚, Celso Grebogid. Level spacing statistics for two-dimensional massless Dirac billiards[J]. 中国物理B, 2014, 23(7): 70507-070507.

Huang Liang (黄亮), Xu Hong-Ya (徐洪亚), Lai Ying-Cheng (来颖诚), Celso Grebogi. Level spacing statistics for two-dimensional massless Dirac billiards[J]. Chin. Phys. B, 2014, 23(7): 70507-070507.

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Level spacing statistics for two-dimensional massless Dirac billiards

Level spacing statistics for two-dimensional massless Dirac billiards

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