Numerical methods for fluctuation driven interactions between dielectrics

TL;DR

This paper introduces a numerical approach to compute thermal Casimir interactions between fluctuating dielectric materials, addressing divergences and validating results with analytic solutions for parallel plates.

Contribution

It presents a discretized theoretical framework for thermal Casimir interactions, including divergence handling and numerical methods validated against analytic solutions.

Findings

Validated numerical methods with analytic parallel plate results

Calculated vertical and lateral Casimir forces for grooved structures

Addressed divergence issues related to system size and discretization

Abstract

We develop a discretized theory of thermal Casimir interactions to numerically calculate the interactions between fluctuating dielectrics. From a constrained partition function we derive a surface free energy, while handling divergences that depend on system size and discretization. We derive analytic results for parallel plate geometry in order to check the convergence of the numerical methods. We use the method to calculate vertical and lateral Casimir forces for a set of grooves.