Distribution of eigenvalues for the modular group

被引：21

作者：

Bogomolny, E ^{[1
]}

Leyvraz, F ^{[1
]}

Schmit, C ^{[1
]}

机构：

[1] LD LANDAU THEORET PHYS INST, CHERNOGOLOVKA 142432, RUSSIA

来源：

COMMUNICATIONS IN MATHEMATICAL PHYSICS | 1996年 / 176卷 / 03期

关键词：

D O I：

10.1007/BF02099251

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

The two-point correlation functions of energy levels for free motion on the modular domain, both with periodic and Dirichlet boundary conditions, are explicitly computed using a generalization of the Hardy-Littlewood method. It is shown that in the limit of small separations they show an uncorrelated behaviour and agree with the Poisson distribution but they have prominent number-theoretical oscillations at larger scale. The results agree well with numerical simulations.

引用

页码：577 / 617

页数：41

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