Geothermal Casimir phenomena for the sphere-plate and cylinder-plate configurations

TL;DR

This paper explores how geometry and temperature influence the Casimir effect in sphere-plate and cylinder-plate setups, revealing non-monotonic thermal forces and limitations of standard approximation methods at low temperatures.

Contribution

It provides a comprehensive analytical and numerical analysis of thermal Casimir forces in complex geometries, highlighting nontrivial temperature dependence and the breakdown of PFA at low temperatures.

Findings

Thermal forces can become non-monotonic below a critical temperature.

Standard approximation techniques like PFA are invalid at low temperatures.

Thermal fluctuations lead to delocalization of force density at low temperatures.

Abstract

We investigate the nontrivial interplay between geometry and temperature in the Casimir effect for the sphere-plate and cylinder-plate configurations. At low temperature, the thermal contribution to the Casimir force is dominated by this interplay, implying that standard approximation techniques such as the PFA are inapplicable even in the limit of small surface separation. Thermal fluctuations on scales of the thermal wavelength lead to a delocalization of the thermal force density at low temperatures. As a consequence, the temperature dependence strongly differs from naive expectations. Most prominently, thermal forces can develop non-monotonic behavior below a critical temperature. We perform a comprehensive study of such geothermal phenomena in these Casimir geometries, using analytical and numerical worldline techniques for Dirichlet scalar fluctuations.