Numerical evaluation of the Casimir interaction between cylinders

TL;DR

This paper numerically evaluates the Casimir interaction energy for various cylinder configurations, providing analytical corrections and improved numerical methods for small-distance regimes, enhancing understanding of Casimir forces in complex geometries.

Contribution

It introduces new numerical techniques and analytical corrections for Casimir interactions between cylinders, especially at small distances, extending previous approximations.

Findings

Analytical corrections to proximity force approximation up to second order.

Numerical methods for small-distance Casimir energy evaluation.

Relation of cylinder-plane Casimir energy to eccentric cylinder configurations.

Abstract

We numerically evaluate the Casimir interaction energy for configurations involving two perfectly conducting eccentric cylinders and a cylinder in front of a plane. We consider in detail several special cases. For quasi-concentric cylinders, we analyze the convergence of a perturbative evaluation based on sparse matrices. For concentric cylinders, we obtain analytically the corrections to the proximity force approximation up to second order, and we present an improved numerical procedure to evaluate the interaction energy at very small distances. Finally, we consider the configuration of a cylinder in front of a plane. We first show numerically that, in the appropriate limit, the Casimir energy for this configuration can be obtained from that of two eccentric cylinders. Then we compute the interaction energy at small distances, and compare the numerical results with the analytic predictions for the first order corrections to the proximity force approximation.