SEMICLASSICAL FREDHOLM DETERMINANT FOR STRONGLY CHAOTIC BILLIARDS
SEMICLASSICAL FREDHOLM DETERMINANT FOR STRONGLY CHAOTIC BILLIARDS
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强混沌台球的半经典 FREDHOLM 行列式
DOI：
10.1088/0951-7715/12/4/322
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发表时间：
1999
期刊：
影响因子：
1.7
通讯作者：
S. Tasaki
中科院分区：
文献类型：
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作者：
T. Harayama;A. Shudo;S. Tasaki
我们调查的'半经典Fredholm行列式'的强混沌台球来自半经典极限的Fredholm行列式的边界元方法。我们证明了当具有台球边界的周期轨道的反弹数对应于其符号动力学表达式的符号序列的长度时，它与循环扩展的Gutzwiller-Voros zeta函数是相同的。一个凹三角形台球的数值实验表明，该系列定义的半经典Fredholm行列式不绝对收敛，尽管该系列定义的Fredholm行列式的绝对收敛。然而，该系列的行为就像一个渐近系列，和有限的和所获得的系列定义的半经典Fredholm行列式的最佳截断给出了半经典本征能足够精确，使误差的半经典近似是远远小于平均间距的确切本征能。
We investigate the `semiclassical Fredholm determinant' for strongly chaotic billiards derived from the semiclassical limit of the Fredholm determinant of the boundary element method. We show that it is the same as a cycle-expanded Gutzwiller - Voros zeta function when the bounce number of the periodic orbit with the billiard boundary corresponds to the length of the symbolic sequence of its symbolic dynamical expression. A numerical experiment on a `concave triangle billiard' shows that the series defining the semiclassical Fredholm determinant does not converge absolutely in spite of the absolute convergence of the series defining the Fredholm determinant. However, the series behaves like an asymptotic series, and the finite sum obtained by optimal truncation of the series defining the semiclassical Fredholm determinant gives the semiclassical eigenenergies precisely enough such that the error of the semiclassical approximation is much smaller than the mean spacing of the exact eigenenergies.
T.Harayama 和 A.Shudo：“由边界元法导出的 Zeta 函数”
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