Finite Temperature Casimir Effect in the Presence of Extra Dimensions

TL;DR

This paper analyzes the finite temperature Casimir force between parallel plates in a cylinder with extra dimensions, revealing how boundary conditions and fractional orders influence whether the force is attractive or repulsive.

Contribution

It introduces formulas for the Casimir force with fractional Neumann boundary conditions and explores how these conditions affect the force's nature in higher-dimensional settings.

Findings

Casimir force is always attractive under Dirichlet conditions

Force is always repulsive for fractional order > 1/2

Force can be attractive or repulsive for fractional orders < 1/2 depending on parameters

Abstract

We consider the finite temperature Casimir force acting on two parallel plates in a closed cylinder with the same cross section of arbitrary shape in the presence of extra dimensions. Dirichlet boundary conditions are imposed on one plate and fractional Neumann conditions with order between zero (Dirichlet) and one (Neumann) are imposed on the other plate. Formulas for the Casimir force show that it is always attractive for Dirichlet boundary conditions, and is always repulsive when the fractional order is larger than 1/2. For some fractional orders less than 1/2, the Casimir force can be either attractive or repulsive depending on the size of the internal manifold and temperature.