Date and time: 29 November 2000, 16:30

Venue: Room M128, Dept. of Mathematics, Brunel University (Uxbridge)

Speaker: Prof. I V Lerner, School of Physics and Astronomy, Birmingham University

"Non-perturbative results for eigenvalue correlation in Random Matrix Theory within the replica method"

Abstract: A replica method is one of the oldest approaches to the physics of disordered systems. It was suggested specifically for perturbative calculations, and in spite of its success in exactly solving a certain spin model, it was widely believed not to be applicable for non-perturbative considerations. In this talk, I will demonstrate that the method allows one to reproduce exactly non-perturbative results for eigenvalue correlation function in Random Matrix Theory (RMT) or, equivalently, in the theory of noninteracting electrons in disordered media. No mathematical justification for this is suggested, but correct asymptotic results for the three RMT ensembles are not incidental. Although much better methods are available within RMT, the replica method seems to be most promising (if not the only one) for applications to the theory of interacting electrons in disordered media.