Temperature-independent Casimir-Polder forces in arbitrary geometries

TL;DR

This paper demonstrates that the Casimir-Polder potential for particles near conducting objects remains unaffected by temperature variations, simplifying calculations for complex geometries and relevant quantum systems.

Contribution

It establishes the temperature independence of the Casimir-Polder potential in arbitrary geometries for energy eigenstates, providing a compact formula and validity criteria.

Findings

Potential is temperature-independent even at high thermal photon numbers.

Derived a simplified expression for the potential applicable to complex geometries.

Numerical validation near gold spheres and inside cylindrical cavities.

Abstract

We show that the Casimir-Polder potential of a particle in an energy eigenstate at nonretarded distance from a well-conducting body of arbitrary shape is independent of the environment temperature. This is true even when the thermal photon numbers at the relevant atomic transition energies are large. A compact expression is obtained for the temperature-independent potential, which can greatly simplify calculations in nontrivial geometries for experimentally relevant systems such as Rydberg atoms and polar molecules. We give criteria for the validity of our temperature-independent result. They are illustrated by numerical studies of a particle near a gold sphere or inside a gold cylindrical cavity.