Correlation Functions in Disordered Systems

TL;DR

This paper investigates the universal behavior of eigenvalue correlations in disordered systems, extending previous work with a diagrammatic approach to time-dependent and parameter-varying matrices, and analyzing eigenvalue distributions.

Contribution

It introduces a diagrammatic method to analyze eigenvalue correlations in evolving disordered systems, expanding understanding of universal behaviors and eigenvalue distributions.

Findings

Eigenvalue correlations exhibit universal behavior.

The diagrammatic approach effectively analyzes time-dependent matrices.

Eigenvalue distributions are characterized for Hamiltonians with deterministic and random parts.

Abstract

{Recently, we found that the correlation between the eigenvalues of random hermitean matrices exhibits universal behavior. Here we study this universal behavior and develop a diagrammatic approach which enables us to extend our previous work to the case in which the random matrix evolves in time or varies as some external parameters vary. We compute the current-current correlation function, discuss various generalizations, and compare our work with the work of other authors. We study the distribution of eigenvalues of Hamiltonians consisting of a sum of a deterministic term and a random term. The correlation between the eigenvalues when the deterministic term is varied is calculated.}