STATISTICAL PROPERTIES OF RANDOM BANDED MATRICES WITH STRONGLY FLUCTUATING DIAGONAL ELEMENTS

Random banded matrices (RBM's) whose diagonal elements fluctuate more than the off-diagonal elements were introduced recently by Shepelyansk y as a convenient means to model the coherent propagation of two inter acting particles in a random potential. We treat the problem analytica lly by using a mapping onto the same supersymmetric nonlinear a model that was used earlier when considering standard RBM ensemble, but with renormalized parameters. A Lorentzian form of the local density of st ates and a two-scale spatial structure of the eigenfunctions presented recently by Jacquod and Shepelyansky are reproduced by direct calcula tion of the distribution of eigenfunction components.