Kramers' escape problem with anomalous kinetics: non-exponential decay of the survival probability

Systems where multiple trapping or other manifestations of disorder lead to a non-local temporal evolution which results in the macroscopic observatio n of anomalous kinetics, are shown to exhibit a non-exponential, Mittag-Lef fler decay in Kramers-type escape problems. The detailed behaviour of the s urvival probability is studied, and it is demonstrated that the associated escape rate is time dependent, exhibiting a turnover from a self-similar to a logarithmic pattern. Comparisons to experiment, and to local models are drawn. (C) 2000 Elsevier Science B.V. All rights reserved.