Stochastic Dynamics, Memory Effects and Fluctuation-Induced Forces in Correlated Media

The presence of correlations in media gives rise to non-trivial effects on the dynamics of mesoscopic bodies immersed in them. A Gaussian field with a tunable correlation length and following relaxational dynamics provides a minimal model of such a spatio-temporally correlated medium. A linear coupling of the field to a probe particle, modeling, e.g., a colloid, renders the effective dynamics of the probe non-linear and non-Markovian. As we show, in the case of the particle trapped harmonically, e.g., by an optical tweezer, at a distance from a wall at which the field satisfies boundary conditions, the probe experiences a field-mediated interaction with the wall, and the correlation function of its position features a memory-induced contribution which depends on the particle-wall separation. When the particle is instead released from the trap after being dragged at a constant velocity, its trajectory features a recoil – motion in the direction opposite to the drag. When it simultaneously rotates about an axis perpendicular to its translation velocity, it experiences a fluctuation-induced Magnus force, perpendicular to both the rotation axis and its translational velocity. Finally, we extend the discussion of fluctuation-induced forces to the case in which correlations stem from the presence of a non-equilibrium steady state, deriving the Casimir pressure acting on the walls of a three-dimensional slab confining an isothermal binary mixture in the presence of gravity. In all these cases, the phenomena originate from the presence of long-ranged correlations.