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

TL;DR

This paper studies how memory effects influence barrier-crossing in single-file diffusion within a bi-stable potential, revealing that higher barriers amplify memory effects and highlighting their importance in modeling transport phenomena.

Contribution

It demonstrates that memory effects arise from collective modes and vary with the external potential, providing new insights into non-Markovian dynamics in confined systems.

Findings

Memory effects are linked to collective eigenmodes projection.

Higher barriers lead to stronger memory effects.

External potential significantly influences memory behavior.

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 tagged-particle 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 behaviors. Notably and somewhat unexpectedly, at a fixed particle number, we find that the higher the barrier, the stronger the memory effects are. The fact that the external potential alters the memory is important more generally and should be taken into account in applications of generalized Langevin equations. Our results can readily be tested experimentally and may be relevant for understanding transport in biological ion-channels.