Kramers-Kronig relations and the properties of conductivity and permittivity in heterogeneous media

Abstract : The macroscopic electric permittivity of a given medium may depend on frequency, but this frequency dependence cannot be arbitrary, its real and imaginary parts are related by the well-known Kramers-Kronig relations. Here, we show that an analogous paradigm applies to the macroscopic electric conductivity. If the causality principle is taken into account, there exists Kramers-Kronig relations for conductivity, which are mathematically equivalent to the Hilbert transform. These relations impose strong constraints that models of heterogeneous media should satisfy to have a physically plausible frequency dependence of the conductivity and permittivity. We illustrate these relations and constraints by a few examples of known physical media. These extended relations constitute important constraints to test the consistency of past and future experimental measurements of the electric properties of heterogeneous media.
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https://hal.archives-ouvertes.fr/hal-02202095
Contributor : Alain Perignon <>
Submitted on : Wednesday, July 31, 2019 - 3:37:05 PM
Last modification on : Friday, August 2, 2019 - 2:23:36 AM

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  • HAL Id : hal-02202095, version 1
  • ARXIV : 1801.00461

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Claude Bédard, Alain Destexhe. Kramers-Kronig relations and the properties of conductivity and permittivity in heterogeneous media. 2018. ⟨hal-02202095⟩

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