The Casimir force at high temperature

TL;DR

This paper investigates the high-temperature Casimir force between conductors, showing that internal charge fluctuations significantly affect the force and aligning quantum and classical models at large separations.

Contribution

It provides a direct quantum electrodynamics calculation of the Casimir force, demonstrating the importance of internal fluctuations in the high-temperature regime.

Findings

The force at large separation matches classical models when including internal fluctuations.

Internal charge fluctuations inside conductors significantly influence the Casimir force.

The classical boundary condition approach overestimates the force by a factor of two.

Abstract

The standard expression of the high-temperature Casimir force between perfect conductors is obtained by imposing macroscopic boundary conditions on the electromagnetic field at metallic interfaces. This force is twice larger than that computed in microscopic classical models allowing for charge fluctuations inside the conductors. We present a direct computation of the force between two quantum plasma slabs in the framework of non relativistic quantum electrodynamics including quantum and thermal fluctuations of both matter and field. In the semi-classical regime, the asymptotic force at large slab separation is identical to that found in the above purely classical models, which is therefore the right result. We conclude that when calculating the Casimir force at non-zero temperature, fluctuations inside the conductors can not be ignored.