The boundary element approach to Van der Waals interactions

TL;DR

This paper introduces a boundary element method to compute non-retarded Van der Waals interactions for complex-shaped dielectric objects, using surface integrals for efficient and accurate numerical evaluation.

Contribution

It presents a novel boundary element approach that simplifies and generalizes the calculation of Van der Waals forces for arbitrary shapes.

Findings

Validated method against Lifshitz theory

Numerical results for sphere-sphere interactions

Self-interaction of a uniaxial ellipsoid computed

Abstract

We develop a boundary element method to calculate Van der Waals interactions for systems composed of domains of spatially constant dielectric response. We achieve this by rewriting the interaction energy expression exclusively in terms of surface integrals of surface operators. We validate this approach in the Lifshitz case and give numerical results for the interaction of two spheres as well as the van der Waals self-interaction of a uniaxial ellipsoid. Our method is simple to implement and is particularly suitable for a full, non-perturbative numerical evaluation of non-retarded van der Waals interactions between objects of a completely general shape.