Distribution of Eigenvalues for the Modular Group
chao-dyn
2016-08-15 v1 混沌动力学
摘要
The two-point correlation function 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 ion 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
@article{arxiv.chao-dyn/9509019,
title = {Distribution of Eigenvalues for the Modular Group},
author = {E. Bogomolny and F. Leyvraz and C. Schmit},
journal= {arXiv preprint arXiv:chao-dyn/9509019},
year = {2016}
}
备注
72 pages, Latex, the fiogures mentioned in the text are not vital, but can be obtained upon request from the first Author