Dynamics of short time--scale energy relaxation of optical excitations due to electron--electron scattering in the presence of arbitrary disorder
A non--equilibrium occupation distribution relaxes towards the Fermi--Dirac distribution due to electron--electron scattering even in finite Fermi systems. The dynamic evolution of this thermalization process assumed to result from an optical excitation is investigated numerically by solving a Boltzmann equation for the carrier populations using a one--dimensional disordered system. We focus on the short time--scale behavior. The logarithmically long time--scale associated with the glassy behavior of interacting electrons in disordered systems is not treated in our investigation. For weak disorder and short range interaction we recover the expected result that disorder enhances the relaxation rate as compared to the case without disorder. For sufficiently strong disorder, however, we find an opposite trend due to the reduction of scattering probabilities originating from the strong localization of the single--particle states. Long--range interaction in this regime produces a similar effect. The relaxation rate is found to scale with the interaction strength, however, the interplay between the implicit and the explicit character of the interaction produces an anomalous exponent.