Stochastic dynamics of particles in fluctuating correlated fields

The effective dynamics of a colloidal particle immersed in a complex medium is usually described in terms of an overdamped generalized Langevin equation — which is linear — possibly with memory.  However, recent numerical simulations and experiments have shown that this linear model fails, suggesting that the intrinsic dynamics of the probe is actually non-linear. Focussing on the case in which the medium can be described as a fluctuating and correlated Gaussian field linearly coupled to the colloid, we derive such a dynamics and discuss its various consequences. In particular, we consider those on the statistics and the relaxation of the position of a single trapped particle, in and out of equilibrium, on the dynamics of the effective interaction between two particles, and on the stochastic thermodynamics in the presence of driving.

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