Low temperature expansion in the Lifshitz formula

Abstract

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 re-derive 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 topic. The paper includes the derivations and should provide a self contained representation.

Final version, to appear in 'Advances in Mathematical Physics'

References in corpus (4)

• Gradient of the Casimir force between Au surfaces of a sphere and a plate measured using atomic force microscope in a frequency shift technique
• Measurement of the gradient of the Casimir force between a nonmagnetic sphere and a magnetic plate
• Kramers-Kronig relations for plasma-like permittivities and the Casimir force
• Problems in the theory of thermal Casimir force between dielectrics and semiconductors