Casimir Piston of Real Materials and its Application to Multi-Layer Models

TL;DR

This paper derives a generalized formula for the Casimir force on a piston made of real materials within a rectangular box, extending to multi-layer models and finite temperature effects, with conditions for force divergence cancellation.

Contribution

It introduces a comprehensive approach to calculating Casimir forces on real material pistons and applies multi-layer models to analyze finite temperature effects and divergence conditions.

Findings

Derived a formula for Casimir force on real material pistons.

Re-derived Lifshitz formula for finite temperature Casimir force.

Identified conditions for divergence cancellation in multi-layer media.

Abstract

In this article, we derive the formula for the Casimir force acting on a piston made of real material moving inside a perfectly conducting rectangular box. It is shown that by taking suitable limits, one recovers the formula for the Casimir force acting on a perfectly conducting piston or an infinitely permeable piston. Lifshitz formula for finite temperature Casimir force acting on parallel plates made of real materials is re-derived by considering the five-layer model in the context of piston approach. It is observed that the divergences of the Casimir force will only cancel under certain conditions, for example, when the regions separated by the plates are filled with media of the same refractive index.