The distribution of the ratio of consecutive level spacings in random matrix ensembles

Autor:	Atas, Y. Y., Bogomolny, E., Giraud, O., Roux, G.
Rok vydání:	2012
Předmět:	Mathematical Physics Condensed Matter - Statistical Mechanics
Zdroj:	Phys. Rev. Lett. 110, 084101 (2013)
Druh dokumentu:	Working Paper
DOI:	10.1103/PhysRevLett.110.084101
Popis:	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. Comment: 5 pages, 4 figures
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1212.5611 Zobrazit plný text záznamu View this record from Arxiv