Probability distribitions of wigner delay times

Abstract

We present results for the probability distribution of Wigner delay times of a two-dimensional disordered solid, described by a tight-binding Anderson model with diagonal disorder W. Using a numerical transfer matrix approach to yield the scattering matrix s of a finite width lattice, the delay time tau(ij) associated with scattering between two channels i,j is proportional to the energy-derivative of the phase of the s -matrix element s(ij). Positive delay times signify that the particle travels through the system more slowly than for, a perfectly clean system. For large positive tau, the probability distribution P(tau) varies as tau(-alpha), whereas for large negative tau it varies as \tau\(-beta) For ballistic systems where disorder W is small, we find beta approximate to 2 while alpha approximate to 4. With increasing W, the values of beta remain approximately constant, whereas alpha decreases, until for the largest values of W, where the system becomes Anderson localised, alpha approximate to beta approximate to 2.