Casimir forces in the time domain: I. Theory

TL;DR

This paper presents a novel time-domain method using FDTD to compute Casimir forces in various geometries and materials, enabling the use of existing simulation tools for quantum force calculations.

Contribution

It introduces a new FDTD-based approach for calculating Casimir forces that can be applied to arbitrary geometries and materials without modifying existing software.

Findings

Method successfully applied to parallel-plate geometry

Framework adaptable to complex 2D and 3D geometries

Analytical and numerical validation of the approach

Abstract

We introduce a method to compute Casimir forces in arbitrary geometries and for arbitrary materials based on the finite-difference time-domain (FDTD) scheme. The method involves the time-evolution of electric and magnetic fields in response to a set of current sources, in a modified medium with frequency-independent conductivity. The advantage of this approach is that it allows one to exploit existing FDTD software, without modification, to compute Casimir forces. In this manuscript, part I, we focus on the derivation, implementation choices, and essential properties of the time-domain algorithm, considered both analytically and illustrated in the simplest parallel-plate geometry. Part II presents results for more complex two- and three-dimensional geometries.