Relativistic quantum level-spacing statistics in chaotic graphene billiards.
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.
Huang
Liang
L
School of Electrical, Computer and Energy Engineering, Arizona State University, Tempe, Arizona 85287, USA.
Lai
Ying-Cheng
YC
Grebogi
Celso
C
D006108:Graphite / Q000737:chemistry*; D008280:Magnetics; D017711:Nonlinear Dynamics; D016011:Normal Distribution; D011789:Quantum Theory
D006108:Graphite