From multiple scattering to van der Waals interactions: exact results for eccentric cylinders

TL;DR

This paper derives exact formulas for van der Waals and Casimir-Polder interactions between eccentric cylinders using multiple scattering theory, advancing understanding of these forces in complex geometries.

Contribution

It provides novel closed-form expressions for interactions between eccentric cylinders and revisits self-energy calculations for tenuous dielectric cylinders.

Findings

Exact formulas for cylinder interactions derived

Application to eccentric cylinders demonstrated

Self-energy of dielectric cylinders revisited

Abstract

In this paper, dedicated to the career of Iver Brevik, we review the derivation of the retarded van der Waals or Casimir-Polder interaction between polarizable molecules from the general multiple scattering formulation of Casimir interactions between bodies. We then apply this van der Waals potential to examine the interaction between tenuous cylindrical bodies, including eccentric cylinders, and revisit the vanishing self-energy of a tenuous dielectric cylinder. In each case, closed-form expressions are obtained.