Magnetic field corrections to the repulsive Casimir effect at finite temperature

TL;DR

This paper analyzes how a uniform magnetic field influences the finite temperature Casimir effect between parallel plates, revealing conditions under which the Casimir pressure becomes less repulsive.

Contribution

It provides analytic expressions for the Casimir free energy and pressure considering magnetic fields, boundary conditions, and temperature limits, extending understanding of magnetic effects on Casimir forces.

Findings

Magnetic field reduces repulsive Casimir pressure in certain limits.

Analytic formulas derived for free energy and pressure at small distances, high temperatures, and strong fields.

Different magnetic field configurations alter the magnitude of the Casimir force.

Abstract

I investigate the finite temperature Casimir effect for a charged and massless scalar field satisfying mixed (Dirichlet-Neumann) boundary conditions on a pair of plane parallel plates of infinite size. The effect of a uniform magnetic field, perpendicular to the plates, on the Helmholtz free energy and Casimir pressure is studied. The zeta-function regularization technique is used to obtain finite results. Simple analytic expressions are obtained for the zeta function and the free energy, in the limits of small plate distance, high temperature and strong magnetic field. The Casimir pressure is obtained in each of the three limits and the situation of a magnetic field present between and outside the plates, as well as that of a magnetic field present only between the plates is examined. It is discovered that, in the small plate distance and high temperature limits, the repulsive pressure is less when the magnetic field is present between the plates but not outside, than it is when the magnetic field is present between and outside the plates.