Stretched exponential relaxation arising from a continuous sum of exponential decays

Stretched exponential relaxation of a quantity n versus time t according to n=n₀0. 2em{0ex}exp- ({^*t) }^ is ubiquitous in many research fields, where ^* is a characteristic relaxation rate and the stretching exponent is in the range 0<<1. Here we consider systems in which stretched exponential relaxation arises from global relaxation of a system containing independently exponentially relaxing species with a probability distribution P (∕^*, ) of relaxation rates. We study the properties of P (∕^*, ) and their dependence on. Physical interpretations of ^* and, derived from consideration of P (∕^*, ) and its moments, are discussed.