Dynamics of driven flow with exclusion in graphene-like structures

TL;DR

This paper develops a mean-field theory for driven exclusion flow in graphene-like structures, comparing predictions with numerical simulations, and explores how sublattice effects influence dynamics and critical behavior.

Contribution

It introduces a mean-field framework for analyzing exclusion flow in honeycomb networks, revealing conditions under which sublattice structure becomes irrelevant and examining critical dynamics.

Findings

Mean-field predictions align with simulations for specific bond rate combinations.

At critical points, the dynamical exponent approaches the one-dimensional value for large systems.

The theory captures qualitative features and late-time behavior despite some quantitative discrepancies.

Abstract

We present a mean-field theory for the dynamics of driven flow with exclusion in graphenelike structures, and numerically check its predictions. We treat first a specific combination of bond transmissivity rates, where mean field predicts, and numerics to a large extent confirms, that the sublattice structure characteristic of honeycomb networks becomes irrelevant. Dynamics, in the various regions of the phase diagram set by open boundary injection and ejection rates, is then in general identical to that of one-dimensional systems, although some discrepancies remain between mean-field theory and numerical results, in similar ways for both geometries. However, at the critical point for which the characteristic exponent is z = 3/2 in one dimension, the mean-field value z = 2 is approached for very large systems with constant (finite) aspect ratio. We also treat a second combination of bond (and boundary) rates where, more typically, sublattice distinction persists. For the two rate combinations, in continuum or late-time limits, respectively, the coupled sets of mean-field dynamical equations become tractable with various techniques and give a two-band spectrum, gapless in the critical phase. While for the second rate combination quantitative discrepancies between mean-field theory and simulations increase for most properties and boundary rates investigated, theory still is qualitatively correct in general, and gives a fairly good quantitative account of features such as the late-time evolution of density profile differences from their steady-state values.