Almost all eigenfunctions of a rational polygon are uniformly distributed

Details Almost all eigenfunctions of a rational polygon are uniformly distributed Almost all eigenfunctions of a rational polygon are uniformly distributed

2011-11-15

arxiv.org/abs/1111.3583v2

Physics

Mathematical Physics

5 pages, to appear in Journal of Spectral Theory

Scientific paper

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.

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