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Auteurs principaux: Pain, Jean-Christophe, Tacu, Mikael
Format: Preprint
Publié: 2025
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Accès en ligne:https://arxiv.org/abs/2506.14941
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author Pain, Jean-Christophe
Tacu, Mikael
author_facet Pain, Jean-Christophe
Tacu, Mikael
contents In order to obtain the frequency-dependent photo-absorption in a plasma, both the real and imaginary parts of the AC conductivity are required. The real part can be deduced from the knowledge of the static conductivity (given by the Ziman-Evans formula for instance) and the Drude model. The imaginary part, required for the refraction index, can be obtained using the Kramers-Kronig relations. Usually, it is obtained by complex integration in the complex plane of the usual Kramers-Kronig relations, having $ω'-ω$ in the denominator. However, an alternate form of the Kramers-Kronig relation is often used in physics, especially for determining response functions. It has $ω'^2-ω^2$ in the denominator. We provide two determinations of the imaginary part of the conductivity for this latter form, one using a decomposition into simple elements, and the other involving a complex integration in a quarter of the complex plane.
format Preprint
id arxiv_https___arxiv_org_abs_2506_14941
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Imaginary part of the conductivity using Kramers-Kronig relations
Pain, Jean-Christophe
Tacu, Mikael
Plasma Physics
In order to obtain the frequency-dependent photo-absorption in a plasma, both the real and imaginary parts of the AC conductivity are required. The real part can be deduced from the knowledge of the static conductivity (given by the Ziman-Evans formula for instance) and the Drude model. The imaginary part, required for the refraction index, can be obtained using the Kramers-Kronig relations. Usually, it is obtained by complex integration in the complex plane of the usual Kramers-Kronig relations, having $ω'-ω$ in the denominator. However, an alternate form of the Kramers-Kronig relation is often used in physics, especially for determining response functions. It has $ω'^2-ω^2$ in the denominator. We provide two determinations of the imaginary part of the conductivity for this latter form, one using a decomposition into simple elements, and the other involving a complex integration in a quarter of the complex plane.
title Imaginary part of the conductivity using Kramers-Kronig relations
topic Plasma Physics
url https://arxiv.org/abs/2506.14941