Monte-Carlo calculation of the lateral Casimir forces between rectangular gratings within the formalism of lattice quantum field theory

TL;DR

This paper introduces a novel Monte-Carlo approach within lattice quantum electrodynamics to accurately compute lateral Casimir forces between rectangular gratings, improving upon traditional approximation methods.

Contribution

The paper presents a new Monte-Carlo method for Casimir force calculations based on lattice QED, validated on simple geometries and applied to complex gratings.

Findings

Monte-Carlo method agrees with known results for ideal planes

Method provides more accurate force calculations than PFA

Applicable to complex grating geometries

Abstract

We propose a new Monte-Carlo method for calculation of the Casimir forces. Our method is based on the formalism of noncompact lattice quantum electrodynamics. This approach has been tested in the simplest case of two ideal conducting planes. After this the method has been applied to the calculation of the lateral Casimir forces between two ideal conducting rectangular gratings. We compare our calculations with the results of PFA and "Optimal" PFA methods.