Casimir Interaction between a plate and a cylinder

Phys Rev Lett. 2006 Mar 3;96(8):080403. doi: 10.1103/PhysRevLett.96.080403. Epub 2006 Mar 1.

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 approximately L/[H3 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.