Correlations of RMT characteristic polynomials and integrability: Hermitean matrices

Journal Article · Fri Oct 15 00:00:00 EDT 2010 · Annals of Physics (New York)

DOI:https://doi.org/10.1016/j.aop.2010.04.005· OSTI ID:21457132

Kanzieper, Eugene ^[1]

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1. Department of Applied Mathematics, H.I.T. - Holon Institute of Technology, Holon 58102 (Israel)

Integrable theory is formulated for correlation functions of characteristic polynomials associated with invariant non-Gaussian ensembles of Hermitean random matrices. By embedding the correlation functions of interest into a more general theory of {tau} functions, we (i) identify a zoo of hierarchical relations satisfied by {tau} functions in an abstract infinite-dimensional space and (ii) present a technology to translate these relations into hierarchically structured nonlinear differential equations describing the correlation functions of characteristic polynomials in the physical, spectral space. Implications of this formalism for fermionic, bosonic, and supersymmetric variations of zero-dimensional replica field theories are discussed at length. A particular emphasis is placed on the phenomenon of fermionic-bosonic factorisation of random-matrix-theory correlation functions.

• OSTI ID: 21457132
• Journal Information: Annals of Physics (New York), Vol. 325, Issue 10; Other Information: DOI: 10.1016/j.aop.2010.04.005; PII: S0003-4916(10)00069-2; Copyright (c) 2010 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved.; ISSN 0003-4916
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
BOSONS
CORRELATION FUNCTIONS
CORRELATIONS
DIFFERENTIAL EQUATIONS
FERMIONS
HERMITIAN MATRIX
INTEGRAL CALCULUS
INTEGRALS
NONLINEAR PROBLEMS
POLYNOMIALS
QUANTUM FIELD THEORY
RANDOMNESS
SUPERSYMMETRY
EQUATIONS
FIELD THEORIES
FUNCTIONS
MATHEMATICS
MATRICES
SYMMETRY