Work

Distribution of the Ratio of Consecutive Level Spacings in Random Matrix Ensembles

Year: 2013

Type: article

Abstract: We derive expressions for the probability distribution of the ratio of two consecutive level spacings for the classical ensembles of random matrices. This ratio distribution was recently introduced to study spectral properties of many-body problems, as, contrary to the standard level spacing distributions, it does not depend on the local density of states. Our Wigner-like surmises are shown to be very accurate when compared to numerics and exact calculations in the large matrix size limit. Quantitative improvements are found through a polynomial expansion. Examples from a quantum many-body lattice model and from zeros of the Riemann zeta function are presented.

Source: Physical Review Letters

DOI: 10.1103/physrevlett.110.084101

Authors: Y. Y. Atas, E. Bogomolny, O. Giraud, G. Roux

Institutions: Université Paris-Sud, Centre National de la Recherche Scientifique, Laboratoire de Physique Théorique et Modèles Statistiques

Language: English

Topic: Quantum chaos and dynamical systems

Subfield: Statistical and Nonlinear Physics

Field: Physics and Astronomy

Domain: Physical Sciences

Open Access status: green

Funder: Agence Nationale de la Recherche

Award: G1476008508