The Totally Asymmetric Simple Exclusion Process with Langmuir Kinetics

TL;DR

This paper introduces a new driven lattice gas model combining the TASEP with Langmuir kinetics, revealing complex phase behavior, localized domain walls, and critical phenomena analyzed through mean-field and analytic solutions involving Lambert W-functions.

Contribution

It presents a novel model coupling TASEP with Langmuir kinetics, providing a comprehensive phase diagram and analytical solutions for the stationary states and critical properties.

Findings

Discovery of localized domain walls and phase coexistence.

Analytic phase diagram using Lambert W-functions.

Unusual mean-field exponents and localization phenomena.

Abstract

We discuss a new class of driven lattice gas obtained by coupling the one-dimensional totally asymmetric simple exclusion process to Langmuir kinetics. In the limit where these dynamics are competing, the resulting non-conserved flow of particles on the lattice leads to stationary regimes for large but finite systems. We observe unexpected properties such as localized boundaries (domain walls) that separate coexisting regions of low and high density of particles (phase coexistence). A rich phase diagram, with high an low density phases, two and three phase coexistence regions and a boundary independent ``Meissner'' phase is found. We rationalize the average density and current profiles obtained from simulations within a mean-field approach in the continuum limit. The ensuing analytic solution is expressed in terms of Lambert $W$-functions. It allows to fully describe the phase diagram and extract unusual mean-field exponents that characterize critical properties of the domain wall. Based on the same approach, we provide an explanation of the localization phenomenon. Finally, we elucidate phenomena that go beyond mean-field such as the scaling properties of the domain wall.