Why retardation takes more time than relaxation in a linear medium

Josef Jäckle, Ranko Richert

Research output: Contribution to journalArticlepeer-review

30 Scopus citations

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.

Original languageEnglish (US)
Article number031201
JournalPhysical Review E - Statistical, Nonlinear, and Soft Matter Physics
Volume77
Issue number3
DOIs
StatePublished - Mar 18 2008

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Statistics and Probability
  • Condensed Matter Physics

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