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