Casimir interaction between a plate and a cylinder

TL;DR

This paper derives the exact Casimir force between a plate and a cylinder, revealing a weak decay at large separations and highlighting differences in mode densities and temperature effects.

Contribution

It provides the first exact calculation of the Casimir force for a plate-cylinder geometry, bridging the gap between known parallel plate and plate-sphere results.

Findings

Force decays as L/(H^3 ln(H/R)) at large H

Transverse magnetic modes dominate the decay behavior

Finite temperature corrections show qualitative differences

Abstract

We find the exact Casimir force between a plate and a cylinder, a geometry intermediate between parallel plates, where the force is known exactly, and the plate--sphere, where it is known at large separations. The force has an unexpectedly weak decay \sim L/(H^3 \ln(H/R)) at large plate--cylinder separations H (L and R are the cylinder length and radius), due to transverse magnetic modes. Path integral quantization with a partial wave expansion additionally gives a qualitative difference for the density of states of electric and magnetic modes, and corrections at finite temperatures.