Spectral properties of the Laplacian and random matrix theories

O. Bohigas , M.J. Giannoni , C. Schmit

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 motion.

Mots clés: chaos; quantum theory; random processes; elastic reflection; Laplacian; random matrix theories; fluctuation properties; eigenvalues; Dirichlet boundary conditions; stadium; chaotic motion

Domaines: Articles anciens

O. Bohigas, M.J. Giannoni, C. Schmit. Spectral properties of the Laplacian and random matrix theories. Journal de Physique Lettres, 1984, 45 (21), pp.1015-1022. ⟨10.1051/jphyslet:0198400450210101500⟩. ⟨jpa-00232444⟩