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A non--equilibrium occupation distribution relaxes towards the Fermi--Diracdistribution due to electron--electron scattering even in finite Fermi systems.The dynamic evolution of this thermalization process assumed to result from anoptical excitation is investigated numerically by solving a Boltzmann equationfor the carrier populations using a one--dimensional disordered system. Wefocus on the short time--scale behavior. The logarithmically long time--scaleassociated with the glassy behavior of interacting electrons in disorderedsystems is not treated in our investigation.  For weak disorder and short range interaction we recover the expected resultthat disorder enhances the relaxation rate as compared to the case withoutdisorder. For sufficiently strong disorder, however, we find an opposite trenddue to the reduction of scattering probabilities originating from the stronglocalization of the single--particle states. Long--range interaction in thisregime produces a similar effect. The relaxation rate is found to scale withthe interaction strength, however, the interplay between the implicit and theexplicit character of the interaction produces an anomalous exponent.Comment: 4 pages, 3 EPS figure

Dynamics of short-time-scale energy relaxation of optical excitations due to electron-electron scattering in the presence of arbitrary disorder