Mass transport perspective on an accelerated exclusion process: Analysis of augmented current and unit-velocity phases

TL;DR

This paper investigates an accelerated exclusion process using a mass transport perspective, revealing novel phases with augmented current and unit-velocity behavior, supported by simulations and analytical methods.

Contribution

It introduces a detailed analysis of phase emergence in AEP through a mass transport framework, connecting condensation phenomena with phase transitions.

Findings

Identification of homogeneous and segregated phases in AEP

Condensation transition from augmented current to unit-velocity phase

Strong agreement between simulations and theoretical predictions

Abstract

In an accelerated exclusion process (AEP), each particle can "hop" to its adjacent site if empty as well as "kick" the frontmost particle when joining a cluster of size $\ell \leq \ell_\text{max}$. With various choices of the interaction range, $\ell_\text{max}$, we find that the steady state of AEP can be found in a homogeneous phase with augmented currents (AC) or a segregated phase with holes moving at unit velocity (UV). Here we present a detailed study on the emergence of the novel phases, from two perspectives: the AEP and a mass transport process (MTP). In the latter picture, the system in the UV phase is composed of a condensate in coexistence with a fluid, while the transition from AC to UV can be regarded as condensation. Using Monte Carlo simulations, exact results for special cases, and analytic methods in a mean field approach (within the MTP), we focus on steady state currents and cluster sizes. Excellent agreement between data and theory is found, providing an insightful picture for understanding this model system.