Seminarium Fizyki Materii Skondensowanej

In the linear overdamped Langevin equation, the effect of collisions of a mesoscopic particle (e.g., a colloid) with the molecules of the surrounding medium is described by instantaneous friction and a random force modeled by Gaussian white noise, yielding a Markovian dynamics of the particle. Such a description assumes that the motion of the molecules occurs on time-scales much shorter than the one at which the motion of the particle is described.Media undergoing a second-order phase transition exhibit collective fluctuations which are characterized by long-range correlations and macroscopic relaxation times, comparable with the typical time-scale of the motion of a colloidal particle.We introduce a minimal model of a particle coupled to a spatio-temporally correlated medium. The medium is described by a fluctuating Gaussian field with a tunable correlation length $\xi$ which follows relaxational dynamics. The particle-field coupling gives rise to: (i) a memory-induced correction in the particle position correlation function; (ii) in the presence of a wall at which the field vanishes, a repulsive Casimir-like force and an enhancement of the memory; (iii) a recoil --- a backwards motion of a particle released from a trap moving with constant velocity; (iv) the Magnus effect --- a transverse force acting on a spinning particle moving with constant velocity.