Density of states for band random matrices with electric field

We present a long-range hopping tight-binding model in which the ensemble averaged density of states, rho (E), undergoes a gradual transition from a homogeneous form with almost no variation to strongly peaked behaviour as an external electric field grows. The model consists of N*N band random matrices of bandwidth b. The corresponding matrix elements, h_ij, have all vanishing average except on the diagonal where, (h_ii)= alpha i. Here, the parameter alpha plays the role of the electric field. We approximate the behaviour of the width, sigma _E, of the local density of states, rho _L(E), and use it to predict the value of alpha around which the transition is centred.