Inducing oscillations of trapped particles in a near-critical Gaussian field

TL;DR

This paper investigates how two particles in harmonic traps interact and synchronize their motion through a fluctuating medium near a phase transition, especially under external periodic driving, combining analytic, perturbative, and numerical methods.

Contribution

It provides a detailed analysis of the nonlinear response and synchronization phenomena in a nonequilibrium system with field-mediated interactions, extending understanding beyond adiabatic approximations.

Findings

Particles synchronize their motion via the medium-mediated interaction.

The nonlinear response varies with driving frequency, especially far from adiabatic conditions.

The analytic solutions are validated against numerical simulations.

Abstract

We study the nonequilibrium dynamics of two particles confined in two spatially separated harmonic potentials and linearly coupled to the same thermally fluctuating scalar field, a cartoon for optically trapped colloids in contact with a medium close to a continuous phase transition. When an external periodic driving is applied to one of these particles, a nonequilibrium periodic state is eventually reached in which their motion synchronizes thanks to the field-mediated effective interaction, a phenomenon already observed in experiments. We fully characterize the nonlinear response of the second particle as a function of the driving frequency, and in particular far from the adiabatic regime in which the field can be assumed to relax instantaneously. We compare the perturbative, analytic solution to its adiabatic approximation, thus determining the limits of validity of the latter, and we qualitatively test our predictions against numerical simulations.