ONE-DIMENSIONAL RANDOM-WALKS ON A LATTICE WITH ENERGETIC DISORDER

Monte Carlo results are obtained for random walks of excitation on a one-dimensional lattice with a Gaussian energy distribution of site energies. The distribution PSI(t) of waiting times is studied for different degrees of energetic disorder. It is shown that at T = 0, PSI(t) is described by a biexponential dependence and at T not-equal 0 the distribution PSI(t) broadens due to the power-law ''tail'' t-1-gamma that corresponds to the description of PSI(t) in the framework of the continuous-time random walk model. The parameter gamma depends linearly on T for strong (T --> 0) and moderate disorder. For the case of T = 0 the number of new sites S(t) visited by a walker is calculated at t --> infinity. The results are in accordance with Monte Carlo data. The survival probability PHI(t) for strong disorder in the long-time limit is characterized by the power-law dependence PHI(t) approximately t(-beta) with beta=cgamma, where c is the trap concentration and for moderate disorder the decay PHI(t) is faster than t(-gamma).