A note on the density of states of a disordered system with Gaussian random potentials

Abstract

A simple analytical method is presented to obtain an expression for a disordered system with Gaussian random potentials by the use of the path-integral formalism. A variational Ansatz due to Edwards (1970) and to Halperin and Lax is applied. The density of states in the low-energy tail has the usual form D(E) approximately exp(- eta mod E mod nu ) with the power nu varying from (4-d)/2 to 2, where d is the dimensionality of the system, and a fuller form is presented which is in agreement with the numerical calculations by Halperin and Lax (1966 and 1967).