Lateral Casimir forces on parallel plates and concentric cylinders with corugations

TL;DR

This paper provides a detailed perturbative analysis of lateral Casimir forces in noncontact gear configurations involving corrugated parallel plates and concentric cylinders, comparing results with PFA and exact calculations.

Contribution

It introduces a perturbative approach to calculate lateral Casimir forces in complex geometries with corrugations, extending previous models and including new comparisons with existing methods.

Findings

First- and second-order perturbation results for parallel plates.

First-order perturbation results for concentric cylinders.

Comparison with PFA and exact weak coupling calculations.

Abstract

In this paper we are giving a quantitative description of two different configurations for noncontact gears. We consider the solutions from a perturbative calculation for two semitransparent parallel plates and concentric cylinders both with corrugations on the inner surfaces. In the case of corrugated parallel plates we discuss results from first- and second-order perturbation calculation in the corrugation amplitudes and we will concentrate on the first-order perturbation for the case of the corrugated concentric cylinders (the second order calculation is under study), both for the weak and strong couplings. We compare the perturbative results with the results from the PFA and an exact weak coupling calculation.