The Casimir Effect

TL;DR

This paper reviews the Casimir effect, explores microscopic models for force calculations at high temperatures, and discusses related dispersion forces, including van der Waals and critical phenomena, highlighting new insights into force magnitudes and boundary conditions.

Contribution

It introduces microscopic charge fluctuation models for Casimir force calculations, revealing forces are weaker than traditional models and emphasizing the importance of boundary conditions.

Findings

Microscopic models show the force is twice weaker than standard calculations.

Inadequacy of inert boundary conditions in high-temperature regimes.

Exact large-distance atomic correlations at low T in the atomic limit.

Abstract

After a review of the standard calculation of the Casimir force between two metallic plates at zero and non-zero temperatures, we present the study of microscopic models to determine the large-distance asymptotic force in the high-temperature regime. Casimir's conducting plates are modelized by plasmas of interacting charges at temperature T. The charges are either classical, or quantum-mechanical and coupled to a (classical) radiation field. In these models, the force obtained is twice weaker than that arising from standard treatments neglecting the microscopic charge fluctutations inside the bodies. The enforcement of inert boundary conditions on the field in the usual calculations turns out to be inadequate in this regime. Other aspects of dispersion forces are also reviewed. The status of (non-retarded) van der Waals-London forces in a dilute medium of non-zero temperature and density is investigated. In a proper scaling regime called the atomic limit (high dilution and low temperature), one is able to give the exact large-distance atomic correlations up to exponentially small terms as T->0. Retarded van der Waals forces and forces between dielectric bodies are also reviewed. Finally, the Casimir effect in critical phenomena is addressed by considering the free Bose gas. It is shown that the grand-canonical potential of the gas in a slab at the critical value of the chemical potential has finite size corrections of the standard Casimir type. They can be attributed to the existence of long-range order generated by gapless excitations in the phase with broken continuous symmetry.