Regular Article - Theoretical Physics
Drude model and Lifshitz formula
Institute for Theoretical Physics, Universität Leipzig, Box 100 920, 04009, Leipzig, Germany
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Revised: 19 October 2011
Published online: 29 October 2011
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.
© Springer-Verlag / Società Italiana di Fisica, 2011