Relativistic quantum level-spacing statistics in chaotic graphene billiards

Liang Huang, Ying-Cheng Lai, Celso Grebogi

Research output: Contribution to journalArticlepeer-review

43 Citations (Scopus)


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
Article number055203
Number of pages4
JournalPhysical Review. E, Statistical, Nonlinear and Soft Matter Physics
Issue number5
Publication statusPublished - May 2010


  • time-reversal symmetry


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