Computation of Casimir Interactions between Arbitrary 3D Objects with Arbitrary Material Properties

TL;DR

This paper extends a computational method for Casimir forces to include arbitrary material properties, enabling accurate predictions for complex geometries and materials like dielectrics and magnetic substances.

Contribution

The authors develop an extended surface current method that accounts for both electric and magnetic properties, allowing for the calculation of Casimir interactions in more realistic scenarios.

Findings

Predicted Casimir forces between dielectric nanodisks in fluid.

Identified separation thresholds where finite-size effects matter.

Mapped rotational energy landscapes of nanoparticle clusters.

Abstract

We extend a recently introduced method for computing Casimir forces between arbitrarily--shaped metallic objects [M. T. H. Reid et al., Phys. Rev. Lett._103_ 040401 (2009)] to allow treatment of objects with arbitrary material properties, including imperfect conductors, dielectrics, and magnetic materials. Our original method considered electric currents on the surfaces of the interacting objects; the extended method considers both electric and magnetic surface current distributions, and obtains the Casimir energy of a configuration of objects in terms of the interactions of these effective surface currents. Using this new technique, we present the first predictions of Casimir interactions in several experimentally relevant geometries that would be difficult to treat with any existing method. In particular, we investigate Casimir interactions between dielectric nanodisks embedded in a dielectric fluid; we identify the threshold surface--surface separation at which finite--size effects become relevant, and we map the rotational energy landscape of bound nanoparticle diclusters.