Statistical mechanics of passive Brownian particles in a fluctuating harmonic trap

TL;DR

This paper analyzes passive Brownian particles in a stochastic, time-dependent harmonic trap, deriving a stationary distribution as a superposition of Gaussians, revealing equilibrium with quenched disorder.

Contribution

It introduces a novel approach to model passive particles in a fluctuating trap using a third-order Fokker-Planck equation and interprets the stationary state as equilibrium with quenched disorder.

Findings

Stationary distribution as superposition of Gaussian distributions.

System can be viewed as equilibrium with quenched disorder.

Derivation of a third-order differential equation for the system.

Abstract

We consider passive Brownian particles trapped in an "imperfect" harmonic trap. The trap is imperfect because it is randomly turned off and on, and as a result, particles fail to equilibrate. Another way to think about this is to say that a harmonic trap is time-dependent on account of its strength evolving stochastically in time. Particles in such a system are passive and activity arises through external control of a trapping potential, thus, no internal energy is used to power particle motion. A stationary Fokker-Planck equation of this system can be represented as a third-order differential equation, and its solution, a stationary distribution, can be represented as a superposition of Gaussian distributions for different strengths of a harmonic trap. This permits us to interpret a stationary system as a system in equilibrium with quenched disorder.