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Geometry-Temperature Interplay in the Casimir Effect

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.