Memory effects in colloidal motion under confinement and driving
Abstract
The transport of individual particles in inhomogeneous environments is complex and exhibits nonMarkovian responses. The latter may be quantified by a memory function within the framework of the linear generalised Langevin equation (GLE). Here, we exemplify the implications of steady driving on the memory function of a colloidal model system for Brownian motion in a corrugated potential landscape, specifically, for onedimensional motion in a sinusoidal potential. To this end, we consider the overdamped limit of the GLE, which is facilitated by separating the memory function into a singular (Markovian) and a regular (nonMarkovian) part. Relying on exact solutions for the investigated model, we show that the random force entering the GLE must display a bias far from equilibrium, which corroborates a recent general prediction. Based on data for the meansquare displacement (MSD) obtained from Brownian dynamics simulations, we estimate the memory function for different driving strengths and show that already moderate driving accelerates the decay of the memory function by several orders of magnitude in time. We find that the memory may persist on much longer timescales than expected from the convergence of the MSD to its longtime asymptote. Furthermore, the functional form of the memory function changes from a monotonic decay to a nonmonotonic, damped oscillatory behaviour, which can be understood from a competition of confined motion and depinning. Our analysis of the simulation data further reveals a pronounced nonGaussianity, which questions the Gaussian approximation of the random force entering the GLE.
 Publication:

Journal of Physics A Mathematical General
 Pub Date:
 July 2024
 DOI:
 10.1088/17518121/ad5b2d
 arXiv:
 arXiv:2405.12904
 Bibcode:
 2024JPhA...57C5003S
 Keywords:

 generalised Langevin equation;
 Brownian motion;
 nonequilibrium dynamics;
 Condensed Matter  Soft Condensed Matter;
 Condensed Matter  Statistical Mechanics
 EPrint:
 J. Phys. A 57 295003 (2024)