Institut für Theoretische Physik 1, Universität Stuttgart, 70550 Stuttgart, Germany.
Phys Rev E. 2017 Jun;95(6-1):062205. doi: 10.1103/PhysRevE.95.062205. Epub 2017 Jun 9.
Recent investigations on the Hamiltonian of excitons by Schweiner et al.. [Phys. Rev. Lett. 118, 046401 (2017)]PRLTAO0031-900710.1103/PhysRevLett.118.046401 revealed that the combined presence of a cubic band structure and external fields breaks all antiunitary symmetries. The nearest-neighbor spacing distribution of magnetoexcitons can exhibit Poissonian statistics, the statistics of a Gaussian orthogonal ensemble (GOE), or a Gaussian unitary ensemble (GUE) depending on the system parameters. Hence, magnetoexcitons are an ideal system to investigate the transitions between these statistics. Here we investigate the transitions between GOE and GUE statistics and between Poissonian and GUE statistics by changing the angle of the magnetic field with respect to the crystal lattice and by changing the scaled energy known from the hydrogen atom in external fields. Comparing our results with analytical formulas for these transitions derived with random matrix theory, we obtain a very good agreement and thus confirm the Wigner surmise for the exciton system.
施魏纳等人最近对激子的哈密顿量进行了研究。[Phys. Rev. Lett. 118, 046401 (2017)]PRLTAO0031-900710.1103/PhysRevLett.118.046401 表明，立方能带结构和外场的共同存在打破了所有反幺正对称性。磁激子的最近邻间距分布可以表现为泊松统计、高斯正交系综 (GOE) 的统计或高斯幺正系综 (GUE) 的统计，这取决于系统参数。因此，磁激子是研究这些统计之间转变的理想系统。在这里，我们通过改变磁场相对于晶格的角度以及通过改变外场中已知的氢原子的标度能量来研究从 GOE 到 GUE 统计和从泊松到 GUE 统计的转变。将我们的结果与随机矩阵理论推导出的这些转变的解析公式进行比较，我们得到了非常好的一致性，从而证实了 Wigner 假设对于激子系统的适用性。
