Critical statistics in quantum chaos and Calogero-Sutherland model at finite temperature
Abstract
We investigate the spectral properties of a generalized GOE (Gaussian Orthogonal Ensemble) capable of describing critical statistics. The joint distribution of eigenvalues of this model is expressed as the diagonal element of the density matrix of a gas of particles governed by the Calogero-Sutherland Hamiltonian (C-S). Taking advantage of the correspondence between C-S particles and eigenvalues, we show that the number variance of our random matrix model is asymptotically linear with a slope depending on the parameters of the model. Such linear behavior is a signature of critical statistics. This random matrix model may be relevant for the description of spectral correlations of complex quantum systems with a self-similar/fractal Poincar\'e section of its classical counterpart. This is shown in detail for two examples: the anisotropic Kepler problem and a kicked particle in a well potential. In both cases the number variance and the -statistic is accurately described by our analytical results.
Keywords
Cite
@article{arxiv.cond-mat/0204151,
title = {Critical statistics in quantum chaos and Calogero-Sutherland model at finite temperature},
author = {A. M. Garcia-Garcia and J. J. M. Verbaarschot},
journal= {arXiv preprint arXiv:cond-mat/0204151},
year = {2009}
}
Comments
27 pages, 4 figures, modified conclusions in section four