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

We study the nonequilibrium 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 assumes fast field relaxation. The predictions of the analytic, perturbative approach are qualitatively confirmed by numerical simulations.

[1]  T. Schilling,et al.  The interplay between memory and potentials of mean force: A discussion on the structure of equations of motion for coarse-grained observables , 2021, EPL (Europhysics Letters).

[2]  M. Gross Dynamics and steady states of a tracer particle in a confined critical fluid , 2021, Journal of Statistical Mechanics: Theory and Experiment.

[3]  R. Wittkowski,et al.  Projection operators in statistical mechanics: a pedagogical approach , 2019, European Journal of Physics.

[4]  Giovanni Volpe,et al.  Controlling the dynamics of colloidal particles by critical Casimir forces. , 2018, Soft matter.

[5]  A. Maciołek,et al.  Collective behavior of colloids due to critical Casimir interactions , 2017, Reviews of Modern Physics.

[6]  Y. Fujitani Osmotic Suppression of Positional Fluctuation of a Trapped Particle in a Near-Critical Binary Fluid Mixture in the Regime of the Gaussian Model , 2017 .

[7]  Artyom Petrosyan,et al.  Energy Transfer between Colloids via Critical Interactions , 2017, Entropy.

[8]  Y. Fujitani Fluctuation Amplitude of a Trapped Rigid Sphere Immersed in a Near-Critical Binary Fluid Mixture , 2015, 1510.03512.

[9]  V. Démery Diffusion of a particle quadratically coupled to a thermally fluctuating field. , 2013, Physical review. E, Statistical, nonlinear, and soft matter physics.

[10]  J. Brady,et al.  Stress development, relaxation, and memory in colloidal dispersions: Transient nonlinear microrheology , 2013 .

[11]  D. Dean,et al.  Thermal Casimir drag in fluctuating classical fields. , 2011, Physical review. E, Statistical, nonlinear, and soft matter physics.

[12]  D. Dean,et al.  Perturbative path-integral study of active- and passive-tracer diffusion in fluctuating fields. , 2011, Physical review. E, Statistical, nonlinear, and soft matter physics.

[13]  D. Dean,et al.  Diffusion of active tracers in fluctuating fields , 2010, Journal of physics. Condensed matter : an Institute of Physics journal.

[14]  S. Sharma,et al.  The Fokker-Planck Equation , 2010 .

[15]  D. Dean,et al.  Drag forces on inclusions in classical fields with dissipative dynamics , 2010, The European physical journal. E, Soft matter.

[16]  D. Dean,et al.  Drag forces in classical fields. , 2009, Physical review letters.

[17]  Andrea Gambassi,et al.  The Casimir effect: From quantum to critical fluctuations , 2008, 0812.0935.

[18]  J. Brady,et al.  A simple paradigm for active and nonlinear microrheology , 2005 .

[19]  M. Kardar,et al.  The `Friction' of Vacuum, and other Fluctuation-Induced Forces , 1997, cond-mat/9711071.

[20]  U. M. Titulaer,et al.  Some remarks on the adiabatic elimination of fast variables from coupled Langevin equations , 1985 .

[21]  U. M. Titulaer,et al.  The systematic adiabatic elimination of fast variables from a many-dimensional Fokker-Planck equation , 1985 .

[22]  Bertrand I. Halperin,et al.  Theory of dynamic critical phenomena , 1977, Physics Today.

[23]  D. Roberts,et al.  On the attraction between two perfectly conducting plates , 2011 .