A new approach to the density of eigenvalues and localization in a general disordered system

Abstract

The density of states and localization in a potential described by multivariate Gaussian distribution is considered by means of a functional integral method. The method is essentially a W. K. B. type of expansion so that the potential is described by a set of oscillators with random frequencies and positions. An original feature is the detailed statistical description of the random potential and its derivatives by multivariate distribution, which enables the averaging procedure to be deferred to the end of the calculation. The density of states is calculated for a model characteristic of a highly doped semiconductor for a Gaussian auto-correlation function over the whole range of energies and found to be exponential at negative energies and approximately proportional to E ½ for positive energies. The mobility edge is treated by studying the convergence of a random series and a numerical estimate of its position is made for a simple model.