Statistical approach to Casimir-Polder potentials in heterogeneous media

TL;DR

This paper investigates the statistical properties of Casimir-Polder potentials in heterogeneous media using numerical simulations, confirming theoretical predictions and providing insights into the full distribution of the potential.

Contribution

It introduces a numerical approach to analyze Casimir-Polder potentials in complex media and compares results with a simple statistical model, advancing understanding of fluctuation effects.

Findings

Confirmed predictions for mean and standard deviation of the potential

Accessed the full distribution function in dilute media

Validated a pairwise summation model for heterogeneities

Abstract

We explore the statistical properties of the Casimir-Polder potential between a dielectric sphere and a three-dimensional heterogeneous medium, by means of extensive numerical simulations based on the scattering theory of Casimir forces. The simulations allow us to confirm recent predictions for the mean and standard deviation of the Casimir potential, and give us access to its full distribution function in the limit of a dilute distribution of heterogeneities. These predictions are compared with a simple statistical model based on a pairwise summation of the individual contributions of the constituting elements of the medium.