Casimir forces between cylinders and plates

TL;DR

This paper calculates Casimir forces between cylinders and plates, revealing complex interaction behaviors including non-monotonic dependence on separation, using advanced partial wave expansion techniques in quantum electrodynamics.

Contribution

It extends previous work by providing detailed calculations of Casimir interactions involving cylinders and plates, highlighting the weak radius dependence and non-monotonic force behaviors.

Findings

Interactions involving cylinders have a weak logarithmic radius dependence.

Non-monotonic force dependence on object separation was confirmed.

Force behaviors are explained via fluctuating charges and mirror images.

Abstract

We study collective interaction effects that result from the change of free quantum electrodynamic field fluctuations by one- and two-dimensional perfect metal structures. The Casimir interactions in geometries containing plates and cylinders is explicitly computed using partial wave expansions of constrained path integrals. We generalize previously obtained results and provide a more detailed description of the technical aspects of the approach \cite{Emig06}. We find that the interactions involving cylinders have a weak logarithmic dependence on the cylinder radius, reflecting that one-dimensional perturbations are marginally relevant in 4D space-time. For geometries containing two cylinders and one or two plates, we confirm a previously found non-monotonic dependence of the interaction on the object's separations which does not follow from pair-wise summation of two-body forces. Qualitatively, this effect is explained in terms of fluctuating charges and currents and their mirror images.