V. Halpern, APPLICATION OF CONTINUOUS-TIME RANDOM-WALKS TO DIELECTRIC-RELAXATION WITH AGE-DEPENDENT TRANSITION RATES, Journal of physics. Condensed matter, 7(39), 1995, pp. 7687-7698
It is shown that the continuous time random walk (CTRW) method provide
s a simple and natural way of treating problems with age-dependent tra
nsition rates (ADTRs) that arise in many theories of non-exponential d
ielectric relaxation. In particular, ADTRs are especially suitable for
analysing systems in which after any transition from one state to ano
ther there is initially an increased probability of a return transitio
n to the original state. An extreme example of this is provided by a s
ystem 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 re
sults of calculations on some model systems are presented and discusse
d.