Application of continuous time random walks to dielectric relaxation with age-dependent transition rates

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Abstract
It is shown that the continuous time random walk (CTRW) method provides a simple and natural way of treating problems with age-dependent transition rates (ADTRs) that arise in many theories of non-exponential dielectric relaxation. In particular, ADTRs are especially suitable for analysing systems in which after any transition from one state to another there is initially an increased probability of a return transition to the original state. An extreme example of this is provided by a system of independent symmetric two-state dipoles having ADTRs, and for this system the CTRW method provides simple exact results. It follows from these results that the dielectric relaxation of such systems at short times is usually associated with a distribution of ADTRs. The results of calculations on some model systems are presented and discussed.