Relativistic quantum level-spacing statistics in chaotic graphene billiards

Liang Huang, Ying-Cheng Lai, Celso Grebogi

Research output: Contribution to journalArticlepeer-review

37 Scopus citations


An outstanding problem in quantum nonlinear dynamics concerns about the energy-level statistics in experimentally accessible relativistic quantum systems. We demonstrate, using chaotic graphene confinements where electronic motions are governed by the Dirac equation in the low-energy regime, that the level-spacing statistics are those given by Gaussian orthogonal ensemble (GOE) random matrices. Weak magnetic field can change the level-spacing statistics to those of Gaussian unitary ensemble for electrons in graphene. For sufficiently strong magnetic field, the GOE statistics are restored due to the appearance of Landau levels.

Original languageEnglish (US)
Article number055203
JournalPhysical Review E - Statistical, Nonlinear, and Soft Matter Physics
Issue number5
StatePublished - May 28 2010

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Statistics and Probability
  • Condensed Matter Physics

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