Joint probability densities of level spacing ratios in random matrices

Autor: Pierpaolo Vivo, Olivier Giraud, Edoardo Vivo, E. Bogomolny, Y. Y. Atas
Přispěvatelé: Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS), Centre National de la Recherche Scientifique (CNRS)-Université Paris-Sud - Paris 11 (UP11), Departamento de Matemáticas and Grupo Interdisciplinar de Sistemas Complejos (GISC), Universidad Carlos III de Madrid [Madrid] (UC3M)
Rok vydání: 2013
Předmět:
Statistics and Probability
[PHYS.MPHY]Physics [physics]/Mathematical Physics [math-ph]
General Physics and Astronomy
FOS: Physical sciences
01 natural sciences
010305 fluids & plasmas
symbols.namesake
[PHYS.QPHY]Physics [physics]/Quantum Physics [quant-ph]
[MATH.MATH-MP]Mathematics [math]/Mathematical Physics [math-ph]
Joint probability distribution
0103 physical sciences
Statistical physics
[PHYS.COND.CM-SM]Physics [physics]/Condensed Matter [cond-mat]/Statistical Mechanics [cond-mat.stat-mech]
010306 general physics
Quantum
Eigenvalues and eigenvectors
Condensed Matter - Statistical Mechanics
Mathematical Physics
Mathematics
Quantum Physics
Statistical Mechanics (cond-mat.stat-mech)
Statistical and Nonlinear Physics
Mathematical Physics (math-ph)
Riemann zeta function
Modeling and Simulation
symbols
Focus (optics)
Quantum Physics (quant-ph)
Random matrix
Lattice model (physics)
Zdroj: Journal of Physics A: Mathematical and Theoretical
Journal of Physics A: Mathematical and Theoretical, IOP Publishing, 2013, 46, pp.355204
ISSN: 1751-8113
1751-8121
DOI: 10.48550/arxiv.1305.7156
Popis: We calculate analytically, for finite-size matrices, joint probability densities of ratios of level spacings in ensembles of random matrices characterized by their associated confining potential. We focus on the ratios of two spacings between three consecutive real eigenvalues, as well as certain generalizations such as the overlapping ratios. The resulting formulas are further analyzed in detail in two specific cases: the beta-Hermite and the beta-Laguerre cases, for which we offer explicit calculations for small N. The analytical results are in excellent agreement with numerical simulations of usual random matrix ensembles, and with the level statistics of a quantum many-body lattice model and zeros of the Riemann zeta function.
Comment: 20 pages
Databáze: OpenAIRE
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