On the accuracy of the PFA: analogies between Casimir and electrostatic forces

TL;DR

This paper evaluates the accuracy of the Proximity Force Approximation (PFA) in calculating Casimir forces, comparing it with exact and asymptotic results, and explores similarities with electrostatic forces.

Contribution

It provides a comprehensive comparison of PFA accuracy for various geometries, especially cylinder-plane configurations, including next-to-leading order corrections.

Findings

PFA's accuracy varies with geometry and distance.

Asymptotic expansions improve approximation precision.

Casimir and electrostatic forces share similarities and differences.

Abstract

We present an overview of the validity of the Proximity Force Approximation (PFA) in the calculation of Casimir forces between perfect conductors for different geometries, with particular emphasis for the configuration of a cylinder in front of a plane. In all cases we compare the exact numerical results with those of PFA, and with asymptotic expansions that include the next to leading order corrections. We also discuss the similarities and differences between the results for Casimir and electrostatic forces.