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| Auteurs principaux: | , |
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| Format: | Preprint |
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2025
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| Accès en ligne: | https://arxiv.org/abs/2506.14941 |
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| _version_ | 1866915348913061888 |
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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 |