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Drude model and Lifshitz formula

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Abstract

Since nearly 10 years, it has been known that inserting the permittivity of the Drude model into the Lifshitz formula for free energy causes a violation of the third law of thermodynamics. In this paper we show that the standard Matsubara formulation for free energy contains a contribution that is non-perturbative in the relaxation parameter. We argue that the correct formula must have a perturbative expansion and conclude that the standard Matsubara formulation with the permittivity of the Drude model inserted is not correct. We trace the non-perturbative contribution in the complex frequency plane, where it shows up as a self-intersection or a bifurcation of the integration path.

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Authors and Affiliations

  1. Institute for Theoretical Physics, Universität Leipzig, Box 100 920, 04009, Leipzig, Germany

    M. Bordag

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  1. M. Bordag
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Bordag, M. Drude model and Lifshitz formula. Eur. Phys. J. C 71, 1788 (2011). https://doi.org/10.1140/epjc/s10052-011-1788-x

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  • DOI: https://doi.org/10.1140/epjc/s10052-011-1788-x

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