Efficient Evaluation of Casimir Force in Arbitrary Three-dimensional Geometries by Integral Equation Methods

TL;DR

This paper presents a generalized surface integral equation method for efficiently computing Casimir forces in complex three-dimensional geometries by leveraging classical electromagnetics techniques.

Contribution

It extends the surface integral equation approach to 3D geometries for Casimir force evaluation, bridging quantum electrodynamics with classical computational methods.

Findings

Enables efficient computation of Casimir forces in arbitrary 3D structures.

Shows that quantum phenomena can be analyzed using classical electromagnetics techniques.

Provides a framework for practical simulations of Casimir effects in complex geometries.

Abstract

In this paper, we generalized the surface integral equation method for the evaluation of Casimir force in arbitrary three-dimensional geometries. Similar to the two-dimensional case, the evaluation of the mean Maxwell stress tensor is cast into solving a series of three-dimensional scattering problems. The formulation and solution of the three-dimensional scattering problem is well-studied in classical computational electromagnetics. This paper demonstrates that this quantum electrodynamic phenomena can be studied using the knowledge and techniques of classical electrodynamics.