Huang Liang, Lai Ying-Cheng, Grebogi Celso
School of Electrical, Computer and Energy Engineering, Arizona State University, Tempe, Arizona 85287, USA.
Phys Rev E Stat Nonlin Soft Matter Phys. 2010 May;81(5 Pt 2):055203. doi: 10.1103/PhysRevE.81.055203. Epub 2010 May 28.
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.
量子非线性动力学中的一个突出问题涉及实验可及的相对论量子系统中的能级统计。我们利用混沌石墨烯限制条件进行了演示，在该条件下电子运动在低能区由狄拉克方程支配，结果表明能级间距统计符合高斯正交系综（GOE）随机矩阵给出的统计规律。对于石墨烯中的电子，弱磁场可将能级间距统计改变为高斯酉系综的统计规律。对于足够强的磁场，由于朗道能级的出现，GOE统计规律得以恢复。
