Probability distribution relaxation time results

If there is the symmetrical potential profile initial distribution is located at the origin (i.e., xo = 0), then all results concerning the relaxation times will be the same as for the potential profile in which the reflecting wall is at x = 0 and at xo = +0. This coincidence of the relaxation times may be proven in a common case taking into account that the probability current at x = 0 is equal to zero at any instant of time. 

These relations allow the majority of the curves (e, e") = /(w) to be described for dielectrics. In these formulas, the deviation from the ideal curve is explained by relaxation time or probability jump distribution. In fact, the a and P values only describe the curves and cannot easily be connected to the material s physical features. So, the results analysis is often limited to the determination of a distribution function or to an equivalent electrical circuit. 

In real systems, typical decay functions are far from exponential, and loss curves, s (log y), appear much broader than the ones found by the Debye model. A phenomenological approach to deal with this observation is to consider that this enlargement in the response is the result of the existence of a distribution of relaxation times, with a probability density function of p(ln x) ... 

Because of the broad distribution of relaxation times characteristic of the -process, it is probably safer to consider it as a superposition of relaxation processes resulting from reorientations about the long axis of different polar groups on the whole side chain. 

---