Random Matrix Theory and QCD at nonzero chemical potential

Abstract

In this lecture we give a brief review of chiral Random Matrix Theory (chRMT) and its applications to QCD at nonzero chemical potential. We present both analytical arguments involving chiral perturbation theory and numerical evidence from lattice QCD simulations showing that correlations of the smallest Dirac eigenvalues are described by chRMT. We discuss the range of validity of chRMT and emphasize the importance of universality. For chRMT's at $\mu \ne 0$ we identify universal properties of the Dirac eigenvalues and study the effect of quenching on the distribution of Yang-Lee zeros.

13 pages, Latex and 3 postscript figures; Invited talk given at the workshop "QCD at Finite Baryon Density: A Complex System with a Complex Action", Bielefeld, 27-30 April 1998

References in corpus (12)

• Random-Matrix Theory of Quantum Transport
• Random Matrix Theories in Quantum Physics: Common Concepts
• Non-Hermitean Random Matrix Theory: method of hermitization
• Almost-Hermitian Random Matrices: Crossover from Wigner-Dyson to Ginibre eigenvalue statistics
• Directed Quantum Chaos
• Non-Gaussian Non-Hermitean Random Matrix Theory: phase transitions and addition formalism
• Microscopic universality in the spectrum of the lattice Dirac operator
• Quantum Disordered Systems with a Direction
• Universal spectral correlations of the Dirac operator at finite temperature
• Dirac Operator Spectra from Finite-Volume Partition Functions
• Universality of Correlation Functions in Random Matrix Models of QCD
• Statistical properties at the spectrum edge of the QCD Dirac operator

Cited by in corpus (6)

• "Single Ring Theorem" and the Disk-Annulus Phase Transition
• The orthogonal ensemble of random matrices and QCD in three dimensions
• Mixing of orthogonal and skew-orthogonal polynomials and its relation to Wilson RMT
• Quaternionic R transform and non-hermitian random matrices
• Chiral Random Matrix Model at Finite Chemical Potential: Characteristic Determinant and Edge Universality
• Hydrodynamical Description of the QCD Dirac Spectrum at Finite Chemical Potential