非均质介质中Kramers-Kronig关系及电导率和介电常数的性质

C. Bédard, A. Destexhe
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引用次数: 8

摘要

给定介质的宏观介电常数可能依赖于频率,但这种频率依赖关系不能是任意的,它的实部和虚部是由著名的Kramers-Kronig关系联系起来的。在这里,我们证明了一个类似的范例适用于宏观电导率。如果考虑因果关系原理,电导率存在Kramers-Kronig关系,它在数学上等同于希尔伯特变换。这些关系施加了很强的约束,异质介质模型必须满足物理上合理的电导率和介电常数的频率依赖性。我们通过几个已知物理介质的例子来说明这些关系和约束。这些扩展关系构成了重要的约束,以测试过去和未来的实验测量的一致性异质介质的电性能。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Kramers-Kronig relations and the properties of conductivity and permittivity in heterogeneous media
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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