Driven Transport on Parallel Lanes with Particle Exclusion and Obstruction

TL;DR

This paper studies a two-lane driven particle transport model with mutual obstruction, revealing complex phase behavior depending on coupling strength, and provides a theoretical approximation validated by simulations.

Contribution

It extends previous models by analyzing intermediate coupling regimes and offers a quantitative cluster approximation for phase behavior.

Findings

Identifies three distinct regimes based on coupling strength.

Derives a one-site cluster approximation for phase analysis.

Validates theoretical predictions with stochastic simulations.

Abstract

We investigate a driven two-channel system where particles on different lanes mutually obstruct each others motion extending an earlier model by Popkov and Peschel [1]. This obstruction may occur in biological contexts due to steric hinderance where motor proteins carry cargos by `walking' on microtubules. Similarly, the model serves as a description for classical spin transport where charged particles with internal states move unidirectionally on a lattice. Three regimes of qualitatively different behavior are identified depending on the strength of coupling between the lanes. For small and large coupling strengths the model can be mapped to a one-channel problem, whereas a new and rich phase behavior emerges for intermediate ones. We derive an approximate but quantitatively accurate theoretical description in terms of a one-site cluster approximation, and obtain insight into the phase behavior through the current-density relations combined with an extremal-current principle. Our results are confirmed by stochastic simulations. [1] V. Popkov and I. Peschel, Phys. Rev. E 64, 026126 (2001).