Out of equilibrium thermal Casimir effect between Brownian conducting plates

TL;DR

This paper investigates the thermal Casimir effect between two conducting surfaces with Brownian charges at different temperatures, deriving expressions for average and fluctuating forces using a dynamical Debye-Hückel approach.

Contribution

It introduces a dynamical Debye-Hückel framework to analyze out-of-equilibrium thermal Casimir forces between Brownian conducting plates.

Findings

Derived expressions for average force between plates.

Calculated variance of force, including normal and lateral components.

Analyzed out-of-equilibrium thermal fluctuation effects.

Abstract

We study the thermal fluctuation induced interactions between two surfaces containing Brownian charges which are held at different temperatures. Using a dynamical form of Debye-H\"uckel theory implemented within the stochastic equation for the density of mobile Brownian charges, we derive expressions for the average force between the two surfaces as well as its variance. The latter is found both for the normal, of finite mean, as well as the lateral force, of zero mean, between the surfaces.