Finite Temperature Casimir Effect and Dispersion in the Presence of Compactified Extra Dimensions

TL;DR

This paper develops a finite temperature Casimir theory for scalar fields in spaces with extra compactified dimensions, incorporating dispersion effects and a scalar refractive index, with focus on low temperature behavior.

Contribution

It generalizes previous Casimir models by including a scalar refractive index and dispersion in extra dimensions, analyzing low temperature effects and dispersive properties.

Findings

Derived general expressions for free energy and Casimir forces.

Analyzed low temperature behavior of Casimir forces with dispersion.

Calculated medium-induced contributions to free energy and pressure.

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 compacified 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, as this is of main physical interest both for force measurements and also for issues related to entropy and the Nernst theorem. Thereafter, in the second part we analyze dispersive properties, assuming for simplicity q=1, by taking into account dispersion associated with the first Matsubara frequency only. The medium-induced contribution to the free energy, and pressure, is calculated at low temperatures.