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

被引：724

作者：

Atas, Y. Y. ^{[1
]}

Bogomolny, E. ^{[1
]}

Giraud, O. ^{[1
]}

Roux, G. ^{[1
]}

机构：

[1] Univ Paris 11, CNRS, UMR 8626, LPTMS, F-91405 Orsay, France

来源：

PHYSICAL REVIEW LETTERS | 2013年 / 110卷 / 08期

关键词：

RIEMANN ZEROS; SPECTRUM;

D O I：

10.1103/PhysRevLett.110.084101

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

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. DOI: 10.1103/PhysRevLett.110.084101

引用

页数：5

共 27 条

[1]

[Anonymous], 2011, The oxford handbook of random matrix theory

[2]

[Anonymous], P S PURE MATH

[3] LEVEL CLUSTERING IN REGULAR SPECTRUM [J].

BERRY, MV ;

TABOR, M .

PROCEEDINGS OF THE ROYAL SOCIETY OF LONDON SERIES A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES, 1977, 356 (1686) :375-394

[4] An attempt to calculate the number of energy levels of a heavy nucleus [J].

Bethe, HA .

PHYSICAL REVIEW, 1936, 50 (04) :332-341

[5]

Biroli G., ARXIV12117334

[6] RANDOM-MATRIX THEORY AND THE RIEMANN ZEROS .1. 3-POINT AND 4-POINT CORRELATIONS [J].

BOGOMOLNY, EB ;

KEATING, JP .

NONLINEARITY, 1995, 8 (06) :1115-1131

[7] CHARACTERIZATION OF CHAOTIC QUANTUM SPECTRA AND UNIVERSALITY OF LEVEL FLUCTUATION LAWS [J].

BOHIGAS, O ;

GIANNONI, MJ ;

SCHMIT, C .

PHYSICAL REVIEW LETTERS, 1984, 52 (01) :1-4

[8]

Bornemann F, 2010, MATH COMPUT, V79, P871, DOI 10.1090/S0025-5718-09-02280-7

[9] RANDOM-MATRIX PHYSICS - SPECTRUM AND STRENGTH FLUCTUATIONS [J].

BRODY, TA ;

FLORES, J ;

FRENCH, JB ;

MELLO, PA ;

PANDEY, A ;

WONG, SSM .

REVIEWS OF MODERN PHYSICS, 1981, 53 (03) :385-479

[10] Quantum Criticality in an Ising Chain: Experimental Evidence for Emergent E8 Symmetry [J].

Coldea, R. ;

Tennant, D. A. ;

Wheeler, E. M. ;

Wawrzynska, E. ;

Prabhakaran, D. ;

Telling, M. ;

Habicht, K. ;

Smeibidl, P. ;

Kiefer, K. .

SCIENCE, 2010, 327 (5962) :177-180

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