Spectral properties of the Laplacian and random matrix theories
- 1 January 1984
- journal article
- Published by EDP Sciences in Journal de Physique Lettres
- Vol. 45 (21), 1015-1022
- https://doi.org/10.1051/jphyslet:0198400450210101500
Abstract
We investigate the fluctuation properties of the eigenvalues of the Laplacian in two dimensions with Dirichlet boundary conditions on a stadium. They are found to be consistent with the fluctuations of eigenvalues of random matrices (GOE). It is conjectured that this is true for any boundary such that the motion of a free particle elastically reflected by the boundary is a strongly chaotic motionKeywords
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