Geometry-Temperature Interplay in the Casimir Effect

TL;DR

This paper explores how long-range thermal fluctuations significantly influence the Casimir effect in open geometries, revealing enhanced temperature dependencies and limitations of local approximation methods.

Contribution

It introduces the concept of geothermal Casimir phenomena, demonstrating fractional power-law temperature dependencies and the unreliability of local energy-density approximations in open geometries.

Findings

Enhanced power-law temperature dependences in inclined-plates configuration

Numerical evidence for fractional power laws induced by long-range fluctuations

Thermal energy densities are distributed over length scales of 1/T

Abstract

We discuss Casimir phenomena which are dominated by long-range fluctuations. A prime example is given by "geothermal" Casimir phenomena where thermal fluctuations in open Casimir geometries can induce significantly enhanced thermal corrections. We illustrate the underlying mechanism with the aid of the inclined-plates configuration, giving rise to enhanced power-law temperature dependences compared to the parallel-plates case. In limiting cases, we find numerical evidence even for fractional power laws induced by long-range fluctuations. We demonstrate that thermal energy densities for open geometries are typically distributed over length scales of 1/T. As an important consequence, approximation methods for thermal corrections based on local energy-density estimates such as the proximity-force approximation are expected to become unreliable even at small surface separations.