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, hij, have all vanishing average except on the diagonal where, (hii)= 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.