Critical behaviour at the mobility edge of the Anderson model of disordered systems

Abstract

The talk covers the behaviour of a quantum mechanic particle moving in a random potential with special emphasis on the aspect of local gauge-invariance. Symmetry argunents are reviewed which allow the mapping of such a system onto a field theoretic model of interacting matrices. This model yields an expansion of the critical exponents at the mobility edge around the lower critical dimensionality two. Since most of this lecture has already been published as a contribution to the Les Houches institute 1980 “Common Trends in Particle and Condensed Matter Physics” I give here only some new results and refer the reader to reference [1].