Low Temperature Expansion in the Lifshitz Formula

The low temperature expansion of the free energy in a Casimir effect setup is considered in detail. The starting point is the Lifshitz formula in Matsubara representation and the basic method is its reformulation using the Abel-Plana formula making full use of the analytic properties. This provides...

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Main Author: M. Bordag
Format: Article
Language:English
Published: Wiley 2014-01-01
Series:Advances in Mathematical Physics
Online Access:http://dx.doi.org/10.1155/2014/981586
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author M. Bordag
author_facet M. Bordag
author_sort M. Bordag
collection DOAJ
description The low temperature expansion of the free energy in a Casimir effect setup is considered in detail. The starting point is the Lifshitz formula in Matsubara representation and the basic method is its reformulation using the Abel-Plana formula making full use of the analytic properties. This provides a unified description of specific models. We rederive the known results and, in a number of cases, we are able to go beyond. We also discuss the cases with dissipation. It is an aim of the paper to give a coherent exposition of the asymptotic expansions for T→0. The paper includes the derivations and should provide a self-contained representation.
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spelling doaj-art-e65d35fe9c4449e0bdbb5b1c175ebd0a2025-02-03T01:25:42ZengWileyAdvances in Mathematical Physics1687-91201687-91392014-01-01201410.1155/2014/981586981586Low Temperature Expansion in the Lifshitz FormulaM. Bordag0Institute for Theoretical Physics, Universität Leipzig, Postfach 100 920, 04009 Leipzig, GermanyThe low temperature expansion of the free energy in a Casimir effect setup is considered in detail. The starting point is the Lifshitz formula in Matsubara representation and the basic method is its reformulation using the Abel-Plana formula making full use of the analytic properties. This provides a unified description of specific models. We rederive the known results and, in a number of cases, we are able to go beyond. We also discuss the cases with dissipation. It is an aim of the paper to give a coherent exposition of the asymptotic expansions for T→0. The paper includes the derivations and should provide a self-contained representation.http://dx.doi.org/10.1155/2014/981586
spellingShingle M. Bordag
Low Temperature Expansion in the Lifshitz Formula
Advances in Mathematical Physics
title Low Temperature Expansion in the Lifshitz Formula
title_full Low Temperature Expansion in the Lifshitz Formula
title_fullStr Low Temperature Expansion in the Lifshitz Formula
title_full_unstemmed Low Temperature Expansion in the Lifshitz Formula
title_short Low Temperature Expansion in the Lifshitz Formula
title_sort low temperature expansion in the lifshitz formula
url http://dx.doi.org/10.1155/2014/981586
work_keys_str_mv AT mbordag lowtemperatureexpansioninthelifshitzformula