Statistical model for stretched exponential relaxation with backtransfer and leakage

Previous calculations of stretched exponential decay in disordered systems have been extended to cover situations where there is backtransfer and leakage in the relaxation channels. Results are obtained for the relaxation of the macroscopic parameter in situations where the channels are governed by Poisson statistics. Analogous results are obtained for Fermi-Dirac and Bose-Einstein statistics. It is shown that in the continuum limit, all three cases have the same macroscopic decay function. Detailed findings are presented for a model where all channels have the same backtransfer and leakage rates. In this case, the decay function is related to the decay in the absence of backtransfer.