2018/01/01 by Claude Bédard, Alain Destexhe, Bedard, Claude +1
Chemistry · Earth and Planetary Sciences · Engineering · #Disordered Systems and Neural Networks (cond-mat.dis-nn) #Electrical and Bioimpedance Tomography #Electrostatics and Colloid Interactions #FOS: Physical sciences #Geophysical and Geoelectrical Methods
paper · pdf · doi:10.48550/arxiv.1801.00461
openalex publication_date 2018/01/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The macroscopic electric permittivity of a given medium may depend on\nfrequency, but this frequency dependence cannot be arbitrary, its real and\nimaginary parts are related by the well-known Kramers-Kronig relations. Here,\nwe show that an analogous paradigm applies to the macroscopic electric\nconductivity. If the causality principle is taken into account, there exists\nKramers-Kronig relations for conductivity, which are mathematically equivalent\nto the Hilbert transform. These relations impose strong constraints that models\nof heterogeneous media should satisfy to have a physically plausible frequency\ndependence of the conductivity and permittivity. We illustrate these relations\nand constraints by a few examples of known physical media. These extended\nrelations constitute important constraints to test the consistency of past and\nfuture experimental measurements of the electric properties of heterogeneous\nmedia.\n