Single-file diffusion in a bi-stable potential: signatures of memory in the barrier-crossing of a tagged-particle

Abstract

We investigate memory effects in barrier-crossing in the overdamped setting. We focus on the scenario where the hidden degrees of freedom relax on exactly the same time scale as the observable. As a prototypical model we analyze taggedparticle diffusion in a single-file confined to a bi-stable potential. We identify the signatures of memory and explain their origin. The emerging memory is a result of the projection of collective many-body eigenmodes onto the motion of a tagged-particle. We are interested in the 'confining' (all background particles in front of the tagged-particle) and 'pushing' (all background particles behind the tagged-particle) scenarios for which we find non-trivial and qualitatively different relaxation behavior. Notably and somewhat unexpectedly, at fixed particle number we find that the higher the barrier the more prominent are the signatures of memory. Our results can readily be tested experimentally and may be relevant for understanding transport in biological ion-channels.