Parity Effects in Eigenvalue Correlators, Parametric and Crossover Correlators in Random Matrix Models: Application to Mesoscopic systems

This paper summarizes some work I've been doing on eigenvalue correlators of Random Matrix Models which show some interesting behaviour. First we consider matrix models with gaps in there spectrum or density of eigenvalues. The density-density correlators of these models depend on whether N, where N is the size of the matrix, takes even or odd values. The fact that this dependence persists in the large N thermodynamic limit is an unusual property and may have consequences in the study of one electron effects in mesoscopic systems. Secondly, we study the parametric and cross correlators of the Harish Chandra-Itzykson-Zuber matrix model. The analytic expressions determine how the correlators change as a parameter (e.g. the strength of a perturbation in the hamiltonian of the chaotic system or external magnetic field on a sample of material) is varied. The results are relevant for the conductance fluctuations in disordered mesoscopic systems.