On the eigenvalue spacing distribution for a point scatterer on the flat torus
Mathematical Physics
2014-03-24 v1 Analysis of PDEs
math.MP
Spectral Theory
Abstract
We study the level spacing distribution for the spectrum of a point scatterer on a flat torus. In the 2-dimensional case, we show that in the weak coupling regime the eigenvalue spacing distribution coincides with that of the spectrum of the Laplacian (ignoring multiplicties), by showing that the perturbed eigenvalues generically clump with the unperturbed ones on the scale of the mean level spacing. We also study the three dimensional case, where the situation is very different.
Cite
@article{arxiv.1208.5920,
title = {On the eigenvalue spacing distribution for a point scatterer on the flat torus},
author = {Zeev Rudnick and Henrik Ueberschaer},
journal= {arXiv preprint arXiv:1208.5920},
year = {2014}
}
Comments
25 pages