Non-universal spectral rigidity of quantum pseudo-integrable billiards
Non-universal spectral rigidity of quantum pseudo-integrable billiards
复制标题
量子赝可积台球的非通用谱刚性
DOI：
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发表时间：
1996
期刊：
影响因子：
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通讯作者：
S. Jain
中科院分区：
文献类型：
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作者：
H. D. Parab;S. Jain
我们获得了伪可积台球的 Dyson-Mehta 统计量，并表明它是非通用的，但具有普遍趋势，而且这种趋势与可积台球的趋势相似。我们提出了一个基于精确的半经典计算和周期轨道扩散定律的公式，该公式为 L 的整个范围提供了刚性。为了巩固我们的理论，我们讨论了几个与数值结果完全一致的例子，以及非普遍性的根本原因。
We obtain the Dyson - Mehta -statistic for pseudo-integrable billiards and show that it is non-universal with a universal trend, also that this trend is similar to the one for integrable billiards. We present a formula, based on exact semiclassical calculations and the proliferation law of periodic orbits, which gives rigidity for the entire range of L. To consolidate our theory, we discuss several examples finding complete agreement with the numerical results, and also the underlying fundamental reasons for the non-universality.