Thouless energy in QCD and effects of diffusion modes on level correlations of Dirac operator

TL;DR

This paper investigates how diffusion modes influence the correlations of Dirac eigenvalues in QCD, revealing non-universal behaviors characterized by Thouless energy through an extended chiral random matrix model.

Contribution

It introduces an extended chiral random matrix model that includes spatial dependence to analyze diffusion effects on Dirac eigenvalue correlations in QCD.

Findings

Analytical expressions for level correlation functions with diffusion effects.

Identification of Thouless energy as a key scale for non-universal behavior.

Pion mode responsible for diffusion effects in the QCD vacuum.

Abstract

The correlations of the QCD Dirac eigenvalues are studied with use of an extended chiral random matrix model. The inclusion of spatial dependence which the original model lacks enables us to investigate the effects of diffusion modes. We get analytical expressions of level correlation functions with non-universal behavior caused by diffusion modes which is characterized by Thouless energy. Pion mode is shown to be responsible for these diffusion effects when QCD vacuum is considered a disordered medium.