Finite temperature Casimir pistons for electromagnetic field with mixed boundary conditions and its classical limit

TL;DR

This paper analyzes the finite temperature Casimir force on a 2D electromagnetic piston with mixed and pure boundary conditions, revealing force behaviors and classical limits at high temperatures.

Contribution

It provides the first detailed analysis of Casimir pistons with mixed boundary conditions at finite temperature, highlighting force tendencies and classical limits.

Findings

Mixed boundary conditions lead to restoring forces towards equilibrium.

Pure boundary conditions cause forces pulling the piston towards the nearest wall.

Force magnitude increases linearly with temperature at high temperatures.

Abstract

In this paper, the finite temperature Casimir force acting on a two-dimensional Casimir piston due to electromagnetic field is computed. It was found that if mixed boundary conditions are assumed on the piston and its opposite wall, then the Casimir force always tends to restore the piston towards the equilibrium position, regardless of the boundary conditions assumed on the walls transverse to the piston. In contrary, if pure boundary conditions are assumed on the piston and the opposite wall, then the Casimir force always tend to pull the piston towards the closer wall and away from the equilibrium position. The nature of the force is not affected by temperature. However, in the high temperature regime, the magnitude of the Casimir force grows linearly with respect to temperature. This shows that the Casimir effect has a classical limit as has been observed in other literatures.