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.
|Physical Review E - Statistical, Nonlinear, and Soft Matter Physics
|Published - May 28 2010
ASJC Scopus subject areas
- Statistical and Nonlinear Physics
- Statistics and Probability
- Condensed Matter Physics