Drude model and Lifshitz formula

Details Drude model and Lifshitz formula Drude model and Lifshitz formula

2011-10-21

arxiv.org/abs/1110.4819v1

Eur. Phys. J. C, 71:1788, 2011

Physics

Quantum Physics

accepted for publication in EPJC

Scientific paper

Since nearly 10 years, it is 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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