Spectral form factor of hyperbolic systems: leading off-diagonal approximation
Spectral form factor of hyperbolic systems: leading off-diagonal approximation
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双曲系统的谱形状因子：领先的非对角线近似
DOI：
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发表时间：
2003
期刊：
影响因子：
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通讯作者：
D. Spehner
中科院分区：
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作者：
D. Spehner
利用周期轨道理论，在半经典极限下研究了具有时间反演对称性的量子哈密顿系统的谱涨落。研究发现，如果长周期轨道是双曲线且在相空间中均匀分布，则谱形状因子 K(τ) 与以海森堡时间为单位测量的时间 τ 中包含的二阶随机矩阵理论的 GOE 预测一致（领先的非对角近似）。我们的方法基于 Sieber 和 Richter 最近发现的周期轨道相关机制 (2001 Phys. Scr. T 90 128)。通过在相空间中重新表述这些作者的理论，他们关于具有恒定负曲率的黎曼曲面上的自由运动的结果被扩展到具有两个自由度的一般哈密顿双曲系统。
The spectral fluctuations of a quantum Hamiltonian system with time-reversal symmetry are studied in the semiclassical limit by using periodic-orbit theory. It is found that, if long periodic orbits are hyperbolic and uniformly distributed in phase space, the spectral form factor K(τ) agrees with the GOE prediction of random-matrix theory up to second order included in the time τ measured in units of the Heisenberg time (leading off-diagonal approximation). Our approach is based on the mechanism of periodic-orbit correlations discovered recently by Sieber and Richter (2001 Phys. Scr. T 90 128). By reformulating the theory of these authors in phase space, their result on the free motion on a Riemann surface with constant negative curvature is extended to general Hamiltonian hyperbolic systems with two degrees of freedom.