Chaotic dynamics and the GOE-GUE transition
Chaotic dynamics and the GOE-GUE transition
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DOI：
10.1088/0951-7715/8/2/005
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发表时间：
1995-03
期刊：
影响因子：
1.7
通讯作者：
O. Bohigas;M. Giannoni;A. M. Almeida;C. Schmit
中科院分区：
文献类型：
--
作者：
O. Bohigas;M. Giannoni;A. M. Almeida;C. Schmit
经典混沌系统的能级统计涨落被认为与高斯矩阵系综的能级统计涨落一致。从高斯正交系综（GOE）到高斯酉系综（GUE）的转变，随着时间反转对称性的破坏，是已知的。从半经典周期轨道理论出发，导出了两点相关函数的渐近形式，给出了跃迁参数的动态表达式。对恒定磁场中混沌台球的相关函数的数值计算表明，随着能级间距的增加，从GUE行为到GOE行为有明显的交叉，与理论预测一致。
The statistical fluctuations of the energy levels of classically chaotic systems are believed to coincide with those of Gaussian matrix ensembles. The transition from the Gaussian orthogonal ensemble (GOE) to the Gaussian unitary ensemble (GUE), as the time-reversal symmetry is broken, is known exactly. The asymptotic form of the two-point correlation function is derived from semiclassical periodic orbit theory, leading to a dynamical evaluation of the transition parameter. Numerical calculations of the correlation function for a chaotic billiard in a constant magnetic field reveal a clear crossover from GUE behaviour to GOE as the level separation is increased, in agreement with the theoretical prediction.