Non-monotonic thermal Casimir force from geometry-temperature interplay

TL;DR

This paper reveals that thermal Casimir forces can exhibit non-monotonic behavior due to geometry-temperature interplay, with forces increasing at certain distances below a critical temperature, explained through the worldline approach.

Contribution

It demonstrates the emergence of non-monotonic thermal Casimir forces in standard geometries, highlighting the role of fluctuation reweighting and providing a transparent worldline interpretation.

Findings

Thermal Casimir force can increase with distance below a critical temperature.

Non-monotonic behavior arises from geometry-temperature interplay.

Worldline picture clarifies the underlying mechanism.

Abstract

The geometry dependence of Casimir forces is significantly more pronounced in the presence of thermal fluctuations due to a generic geometry-temperature interplay. We show that the thermal force for standard sphere-plate or cylinder-plate geometries develops a non-monotonic behavior already in the simple case of a fluctuating Dirichlet scalar. In particular, the attractive thermal force can increase for increasing distances below a critical temperature. This anomalous behavior is triggered by a reweighting of relevant fluctuations on the scale of the thermal wavelength. The essence of the phenomenon becomes transparent within the worldline picture of the Casimir effect.