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Casimir interaction between a plate and a cylinder

T. Emig·R. L. Jaffe·M. Kardar·A. Scardicchio
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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.

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T. Emig, R. L. Jaffe, M. Kardar, A. Scardicchio. 2006-01-03. Casimir interaction between a plate and a cylinder. https://doi.org/10.1103/physrevlett.96.080403

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