Numerical studies of Casimir interactions

TL;DR

This paper presents numerical methods to analyze Casimir interactions between dielectric objects in 2D and 3D, highlighting the use of sparse matrix factorizations for complex geometries and interaction regimes.

Contribution

It introduces advanced numerical techniques, including sparse matrix factorizations, to study Casimir forces in diverse dielectric configurations and regimes.

Findings

Sparse matrix factorizations enable efficient 3D Casimir calculations.

The study maps the crossover between non-retarded and retarded interactions in 2D.

Interaction measurements with rough surfaces agree with scaling predictions.

Abstract

We study numerically the Casimir interaction between dielectrics in both two and three dimensions. We demonstrate how sparse matrix factorizations enable one to study torsional interactions in three dimensions. In two dimensions we study the full cross-over between non-retarded and retarded interactions as a function of separation. We use constrained factorizations in order to measure the interaction of a particle with a rough dielectric surface and compare with a scaling argument.