The low temperature corrections to the Casimir force between a sphere and a plane

TL;DR

This paper calculates low temperature corrections to the Casimir force between a sphere and a plane for scalar and electromagnetic fields, considering various boundary conditions and material properties.

Contribution

It provides a comprehensive analysis of low temperature effects on Casimir forces for different boundary conditions and material models, extending previous work.

Findings

Derived explicit formulas for low temperature corrections

Analyzed effects for scalar and electromagnetic fields

Compared results for different boundary conditions and materials

Abstract

We calculate the low temperature corrections to the free energy for a sphere in front of a plane. First, the scalar field obeying Dirichet or Neumann boundary conditions is considered. Second, the electromagnetic field is studied, the sphere being perfectly conducting and being a dielectric ball with both, constant permittivity and permittivity of the plasma model.