Semiclassical approach to discrete symmetries in quantum chaos
Semiclassical approach to discrete symmetries in quantum chaos
复制标题
量子混沌中离散对称性的半经典方法
DOI：
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发表时间：
2012
期刊：
影响因子：
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通讯作者：
M. Sieber
中科院分区：
文献类型：
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作者：
C. H. Joyner;S. Müller;M. Sieber
我们使用半经典方法来评估具有离散几何对称性的量子混沌系统的谱两点相关函数。这些系统的能谱可以分为与相应对称群的不可约表示相关的子谱。我们表明，对于（无自旋）时间反转不变系统，这些子谱内的统计数据取决于不可约表示的类型。对于实数表示，谱统计与随机矩阵理论（RMT）的高斯正交系综一致，而复数表示对应于高斯酉系综（GUE）。对于没有时间反转不变性的系统，所有子谱都显示 GUE 统计数据。非简并子谱之间不存在相关性。我们的技术概括了量子混沌半经典方法的最新发展，使人们能够与 RMT 预测的两点相关函数完全一致，包括振荡贡献。
We use semiclassical methods to evaluate the spectral two-point correlation function of quantum chaotic systems with discrete geometrical symmetries. The energy spectra of these systems can be divided into subspectra that are associated with irreducible representations of the corresponding symmetry group. We show that for (spinless) time-reversal invariant systems, the statistics inside these subspectra depends on the type of irreducible representation. For real representations the spectral statistics agrees with those of the Gaussian orthogonal ensemble of random matrix theory (RMT), whereas complex representations correspond to the Gaussian unitary ensemble (GUE). For systems without time-reversal invariance, all subspectra show GUE statistics. There are no correlations between non-degenerate subspectra. Our techniques generalize recent developments in the semiclassical approach to quantum chaos allowing one to obtain full agreement with the two-point correlation function predicted by RMT, including oscillatory contributions.
影响因子：
8.6
作者：
Heusler, Stefan;Mueller, Sebastian;Haake, Fritz
通讯作者：
Haake, Fritz