Chiral random matrix theory and effective theories of QCD Original Research Article

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 orginal 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 disorderd medium.