Low Temperature Expansion in the Lifshitz Formula

Abstract EN

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.