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

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.

33 pages, 11 figures

References in corpus (5)

• The Casimir effect: from quantum to critical fluctuations
• Projection operators in statistical mechanics: a pedagogical approach
• Energy transfer between colloids via critical interactions
• Dynamics and steady states of a tracer particle in a confined critical fluid
• Non-Markovian systems out of equilibrium: Exact results for two routes of coarse graining