Almost all eigenfunctions of a rational polygon are uniformly distributed
Mathematical Physics
2011-12-06 v2 math.MP
Spectral Theory
Chaotic Dynamics
Abstract
We consider an orthonormal basis of eigenfunctions of the Dirichlet Laplacian for a rational polygon. The modulus squared of the eigenfunctions defines a sequence of probability measures. We prove that this sequence contains a density-one subsequence that converges to Lebesgue measure.
Keywords
Cite
@article{arxiv.1111.3583,
title = {Almost all eigenfunctions of a rational polygon are uniformly distributed},
author = {Jens Marklof and Zeev Rudnick},
journal= {arXiv preprint arXiv:1111.3583},
year = {2011}
}
Comments
5 pages, to appear in Journal of Spectral Theory