For a linear medium, it is shown that the ratio of average relaxation to retardation time is given by the ratio of the high- to the low-frequency limit of the dielectric constants, τM / τε = ε / εs. This statement holds for dispersive dynamics, i.e., it is not limited to the special case of exponential responses. A second general relation is found for the relative relaxation-time dispersions, which implies that the relaxation is always more stretched than its retardation counterpart. A difference equation for the charge buildup is established which provides a rationale for why retardation requires more time than its relaxation counterpart. According to the equation, the slowness of the charge buildup is due to a renewal process of continuous re-investment of potential made redundant by relaxation. The relevance of the results to experimental situations is also discussed.
|Physical Review E - Statistical, Nonlinear, and Soft Matter Physics
|Published - Mar 18 2008
ASJC Scopus subject areas
- Statistical and Nonlinear Physics
- Statistics and Probability
- Condensed Matter Physics