Numerical methods for computing Casimir interactions

TL;DR

This paper reviews various numerical methods for calculating Casimir forces between objects of arbitrary shapes and materials, highlighting their connections to classical electromagnetism techniques and categorizing approaches based on problem setup, basis, and solution methods.

Contribution

It systematically categorizes and explains classical computational techniques adapted for Casimir force calculations, facilitating their application to complex geometries and materials.

Findings

Classical electromagnetism methods can be adapted for Casimir computations.

Different approaches are classified by problem type, basis, and solution technique.

The review highlights modifications needed for classical methods to handle Casimir physics.

Abstract

We review several different approaches for computing Casimir forces and related fluctuation-induced interactions between bodies of arbitrary shapes and materials. The relationships between this problem and well known computational techniques from classical electromagnetism are emphasized. We also review the basic principles of standard computational methods, categorizing them according to three criteria---choice of problem, basis, and solution technique---that can be used to classify proposals for the Casimir problem as well. In this way, mature classical methods can be exploited to model Casimir physics, with a few important modifications.