Statistical mechanics of passive Brownian particles in a fluctuating harmonic trap
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.
Keywords
Cite
@article{arxiv.2407.12213,
title = {Statistical mechanics of passive Brownian particles in a fluctuating harmonic trap},
author = {Derek Frydel},
journal= {arXiv preprint arXiv:2407.12213},
year = {2024}
}
Comments
11 pages, 7 figures