The Stochastic Casimir Effect

TL;DR

This paper models a classical vacuum using annihilating Brownian motions with immigration, demonstrating an attractive force between walls that decays exponentially with distance, akin to a classical Casimir effect.

Contribution

It introduces a novel stochastic model of a classical vacuum and characterizes the Casimir-like force between boundaries within this framework.

Findings

The force between walls decays exponentially with separation.

The model captures a classical Casimir effect in a stochastic setting.

The system exhibits an attractive force due to particle interactions.

Abstract

We model the one-dimensional `classical' vacuum by a system of annihilating Brownian motions on $\mathbb{R}$ with pairwise immigration. A pair of reflecting or absorbing walls placed in such a vacuum at separation $L$ experiences an attractive force which decays exponentially with $L$. This phenomenon can be regarded as a purely classical Casimir effect for a system of interacting Brownian motions.