Nonmonotonic effects of parallel sidewalls on Casimir forces between cylinders

TL;DR

This paper investigates how the Casimir force between two metal cylinders is affected by nearby metal plates, revealing a nonmonotonic, multi-body phenomenon that cannot be explained by simple two-body interactions.

Contribution

The study demonstrates the nonmonotonic dependence of Casimir forces on sidewall separation and explains it through screening effects, extending previous results to cylinders and multiple sidewalls.

Findings

Casimir force between cylinders varies nonmonotonically with sidewall distance.

The nonmonotonicity arises from charge and current screening effects.

Force dependence also affects cylinder-plate interactions.

Abstract

We analyze the Casimir force between two parallel infinite metal cylinders, with nearby metal plates (sidewalls), using complementary methods for mutual confirmation. The attractive force between cylinders is shown to have a nonmonotonic dependence on the separation to the plates. This intrinsically multi-body phenomenon, which occurs with either one or two sidewalls (generalizing an earlier result for squares between two sidewalls), does not follow from any simple two-body force description. We can, however, explain the nonmonotonicity by considering the screening (enhancement) of the interactions by the fluctuating charges (currents) on the two cylinders, and their images on the nearby plate(s). Furthermore, we show that this effect also implies a nonmonotonic dependence of the cylinder-plate force on the cylinder-cylinder separation.