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

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 the Thouless energy. The pion mode is shown to be responsible for these diffusion effects when the QCD vacuum is considered a disordered medium