Periodic-orbit theory of universal level correlations in quantum chaos
Periodic-orbit theory of universal level correlations in quantum chaos
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DOI：
10.1088/1367-2630/11/10/103025
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发表时间：
2009-10-12
影响因子：
3.3
通讯作者：
Haake, Fritz
中科院分区：
文献类型：
--
作者：
Mueller, Sebastian;Heusler, Stefan;Haake, Fritz
利用Gutzwiller的半经典双轨道理论，我们证明了经典极限为完全混沌的量子系统的能级密度两点关联器的普适行为。我们超越以前的工作，建立完整的相关器，使其傅立叶变换，频谱形状因子，是确定所有的时间，低于和高于海森堡时间。我们涵盖了动力学与时间反演不变性（从正交和酉对称类）。在我们的推理中，一个关键步骤是用一个矩阵积分来求和π-轨道展开，就像从随机矩阵理论的sigma模型中已知的那样。
Using Gutzwiller's semiclassical periodic-orbit theory, we demonstrate universal behavior of the two-point correlator of the density of levels for quantum systems whose classical limit is fully chaotic. We go beyond previous work in establishing the full correlator such that its Fourier transform, the spectral form factor, is determined for all times, below and above the Heisenberg time. We cover dynamics with and without time-reversal invariance (from the orthogonal and unitary symmetry classes). A key step in our reasoning is to sum the periodic-orbit expansion in terms of a matrix integral, like the one known from the sigma model of random matrix theory.