Why retardation takes more time than relaxation in a linear medium

Abstract

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.