Nonequilibrium relaxation of a trapped particle in a near-critical Gaussian field

TL;DR

This paper investigates the non-equilibrium relaxation dynamics of a particle coupled to a near-critical scalar field, revealing universal long-time algebraic decay behaviors near the critical point, confirmed by simulations.

Contribution

It provides a theoretical analysis of the long-time relaxation tails of a trapped particle near a critical point, including universal exponents in arbitrary dimensions.

Findings

Long-time algebraic tails in particle relaxation near criticality

Universal exponents determined for arbitrary dimensions

Qualitative agreement between analytic predictions and numerical simulations

Abstract

We study the non-equilibrium relaxational dynamics of a probe particle linearly coupled to a thermally fluctuating scalar field and subject to a harmonic potential, which provides a cartoon for an optically trapped colloid immersed in a fluid close to its bulk critical point. The average position of the particle initially displaced from the position of mechanical equilibrium is shown to feature long-time algebraic tails as the critical point of the field is approached, the universal exponents of which are determined in arbitrary spatial dimensions. As expected, this behavior cannot be captured by adiabatic approaches which assume fast field relaxation. The predictions of the analytic, perturbative approach are qualitatively confirmed by numerical simulations.