Interplay between geometry and temperature for inclined Casimir plates

TL;DR

This paper explores how the geometry and temperature influence the Casimir effect between inclined plates, revealing unique power-law behaviors at different temperature regimes through worldline formalism analysis.

Contribution

It demonstrates the nontrivial interplay between geometry and temperature in the Casimir effect, identifying new power-law behaviors for inclined plates not seen in parallel configurations.

Findings

High-temperature behavior is linear in T.

Inclined plates exhibit a T^{D-1} force dependence.

Edge effects show a T^{D-0.3} dependence, and torque varies as T^{D-2}.

Abstract

We provide further evidence for the nontrivial interplay between geometry and temperature in the Casimir effect. We investigate the temperature dependence of the Casimir force between an inclined semi-infinite plate above an infinite plate in D dimensions using the worldline formalism. Whereas the high-temperature behavior is always found to be linear in T in accordance with dimensional-reduction arguments, different power-law behaviors at small temperatures emerge. Unlike the case of infinite parallel plates, which shows the well-known T^D behavior of the force, we find a T^{D-1} behavior for inclined plates, and a ~T^{D-0.3} behavior for the edge effect in the limit where the plates become parallel. The strongest temperature dependence ~T^{D-2} occurs for the Casimir torque of inclined plates. Numerical as well as analytical worldline results are presented.