Level spacing statistics for two-dimensional massless Dirac billiards

Huang Liang, Xu Hong-Ya, Lai Ying-Cheng, Celso Grebogi

Research output: Contribution to journalArticlepeer-review

13 Citations (Scopus)


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.

Original languageEnglish
Article number070507
Number of pages12
JournalChinese Physics B
Issue number7
Early online date22 May 2014
Publication statusPublished - Jul 2014


  • quantum chaos
  • level spacing statistics
  • Dirac billiards
  • graphene billiards
  • time-reversal symmetry
  • topological insulators
  • quantum billiards
  • carbon nanotubes
  • magnetic-fields
  • graphene
  • chaos
  • scattering
  • transport
  • phase


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