Inter-particle ratchet effect determines global current of heterogeneous particles diffusing in confinement

TL;DR

This paper presents an exactly solvable model of heterogeneous particles in a confined tube, revealing how differences in particle properties induce a ratchet effect that biases the global current.

Contribution

It introduces a quasi-one-dimensional model where geometrical constraints enable exact solutions, highlighting the ratchet effect driven by particle heterogeneity.

Findings

Current biased towards less diffusive particles

Exact joint gap distribution derived for driven tracers

Quasi-one-dimensionality is key to solvability

Abstract

In a model of $N$ volume-excluding spheres in a $d$-dimensional tube, we consider how differences between particles in their drift velocities, diffusivities, and sizes influence the steady state distribution and axial particle current. We show that the model is exactly solvable when the geometrical constraints prevent any particle from overtaking every other -- a notion we term quasi-one-dimensionality. Then, due to a ratchet effect, the current is biased towards the velocities of the least diffusive particles. We consider special cases of this model in one dimension, and derive the exact joint gap distribution for driven tracers in a passive bath. We describe the relationship between phase space structure and irreversible drift that makes the quasi-one-dimensional supposition key to the model's solvability.