Dyson's Brownian Motion and Universal Dynamics of Quantum Systems

Abstract

We establish a correspondence between the evolution of the distribution of eigenvalues of a $N\times N$ matrix subject to a random Gaussian perturbing matrix, and a Fokker-Planck equation postulated by Dyson. Within this model, we prove the equivalence conjectured by Altshuler et al between the space-time correlations of the Sutherland-Calogero-Moser system in the thermodynamic limit and a set of two-variable correlations for disordered quantum systems calculated by them. Multiple variable correlation functions are, however, shown to be inequivalent for the two cases.

10 pages, revtex

Cited by in corpus (22)

• Random Matrix Theories in Quantum Physics: Common Concepts
• The Statistical Theory of Quantum Dots
• Spectral form factor in a random matrix theory
• On an exactly solvable $B_N$ type Calogero model with nonhermitian PT invariant interaction
• Alternative Technique for "Complex" Spectra Analysis
• Random Matrix Model and the Calogero-Sutherland Model: A Novel Current-Density Mapping
• Universal Parametric Correlations of Eigenfunctions in Chaotic and Disordered Systems
• Spin dependent extension of Calogero-Sutherland model through anyon like representations of permutation operators
• Exact Dynamical Correlations of the 1/r^2 Model
• A Class of Parameter Dependent Commuting Matrices
• Orthogonal Polynomials and Exact Correlation Functions for Two Cut Random Matrix Models
• Universal Spectral Correlation between Hamiltonians with Disorder
• Relaxation of Terrace-width Distributions: Physical Information from Fokker-Planck Time
• Universality of Parametric Spectral Correlations: Local versus Extended Perturbing Potentials
• Parametric Statistics of Individual Energy Levels in Random Hamiltonians
• Spectral Form Factor for Time-dependent Matrix model
• Universal Level dynamics of Complex Systems
• Deformed multi-variable Fokker-Planck equations
• Parametric Ward-Takahashi identity in disordered systems and the integral identity associated with the Calogero-Sutherland model
• Efficient circular Dyson Brownian motion algorithm
• Higher order parametric level statistics in disordered systems
• Parity Effects in Eigenvalue Correlators, Parametric and Crossover Correlators in Random Matrix Models: Application to Mesoscopic systems