1994/12/06 by Ovidiu Costin, Joel L. Lebowitz · 3 citations
Chemistry · Physics and Astronomy · #Molecular spectroscopy and chirality #Quantum chaos and dynamical systems #Theoretical and Computational Physics #chao-dyn #nlin.CD
paper · pdf · doi:10.1103/physrevlett.75.69
13 pages
arxiv created 1994/12/06 · openalex publication_date 1995/07/03 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let N(L) be the number of eigenvalues, in an interval of length L, of a matrix chosen at random from the Gaussian orthogonal, unitary, or symplectic ensembles of N by N matrices, in the limit N\ensuremath→\ensuremath∞. We prove that [N(L)\ensuremath-〈N(L)〉]/√(lnL) has a Gaussian distribution when L\ensuremath→\ensuremath∞. This theorem, which requires control of all the higher moments of the distribution, elucidates numerical and exact results on chaotic quantum systems and on the statistics of zeros of the Riemann zeta function.