Pistons modeled by potentials

TL;DR

This paper investigates the Casimir effect for a piston modeled by a potential in extra dimensions, using zeta function techniques to analyze the functional determinant and force for scalar fields with various potentials.

Contribution

It introduces a formalism for computing the Casimir effect for pistons modeled by arbitrary smooth potentials, extending beyond compact support assumptions.

Findings

Derived expressions for the functional determinant in the presence of a potential

Analyzed the Casimir force for different potential profiles

Provided a general method applicable to various smooth potentials

Abstract

In this article we consider a piston modelled by a potential in the presence of extra dimensions. We analyze the functional determinant and the Casimir effect for this configuration. In order to compute the determinant and Casimir force we employ the zeta function scheme. Essentially, the computation reduces to the analysis of the zeta function associated with a scalar field living on an interval $[0,L]$ in a background potential. Although, as a model for a piston, it seems reasonable to assume a potential having compact support within $[0,L]$, we provide a formalism that can be applied to any sufficiently smooth potential.