Fluctuations of Fluctuation-Induced "Casimir" Forces

TL;DR

This paper analyzes the statistical fluctuations of fluctuation-induced Casimir forces, revealing that their probability distribution is Gaussian with a standard deviation comparable to the mean, impacting experimental measurements.

Contribution

It provides the first detailed computation of the probability distribution of fluctuation-induced forces, highlighting their Gaussian nature and significant fluctuations.

Findings

Force fluctuations are Gaussian centered on the Casimir force.

Standard deviation of force fluctuations can be as large as the mean.

Finite measurement resolution affects the observed force statistics.

Abstract

The force experienced by objects embedded in a correlated medium undergoing thermal fluctuations--the so-called fluctuation--induced force--is actually itself a fluctuating quantity. We compute the corresponding probability distribution and show that it is a Gaussian centered on the well-known Casimir force, with a non-universal standard deviation that can be typically as large as the mean force itself. The relevance of these results to the experimental measurement of fluctuation-induced forces is discussed, as well as the influence of the finite temporal resolution of the measuring apparatus.