Finite temperature Casimir effect and dispersion in the presence of compactified extra dimensions

Abstract

Finite temperature Casimir theory of the Dirichlet scalar field is developed assuming that there is a conventional Casimir setup in physical space with two infinitely large plates separated by a gap R and, in addition, an arbitrary number q of extra compactified dimensions. As a generalization of earlier theory, we assume in the first part of the paper that there is a scalar ‘refractive index’ N filling the whole of the physical space region. After presenting general expressions for free energy and Casimir forces, we focus on the low temperature case, because this is of major physical interest both for force measurements and for issues related to entropy and the Nernst theorem. Thereafter, in the second part we analyze dispersive properties, assuming for simplicity that q=1, by taking into account the dispersion associated with the first Matsubara frequency only. The medium-induced contribution to the free energy, and pressure, is calculated at low temperatures.