Casimir force waves induced by non-equilibrium fluctuations between vibrating plates

TL;DR

This paper investigates how non-equilibrium fluctuations induce time-dependent Casimir-like forces between vibrating plates in a fluid, revealing wave-like stress propagation and resonance effects.

Contribution

It introduces a model for fluctuation-induced forces under non-equilibrium conditions with vibrating boundaries, highlighting wave propagation and resonance phenomena.

Findings

Force exhibits a positive lag time indicating wave-like stress propagation.

Two main force contributions: static-like and resonant dissipation.

Finite propagation speed of stress through the fluid medium.

Abstract

We study the fluctuation-induced, time-dependent force between two plates immersed in a fluid driven out of equilibrium mechanically by harmonic vibrations of one of the plates. Considering a simple Langevin dynamics for the fluid, we explicitly calculate the fluctuation-induced force acting on the plate at rest. The time-dependence of this force is characterized by a positive lag time with respect to the driving, indicating a finite speed of propagation of stress through the medium, reminiscent of waves. We obtain two distinctive contributions to the force, where one may be understood as directly emerging from the corresponding force in the static case, while the other is related to resonant dissipation in the cavity between the plates.