Theoretical Investigation of Totally Asymmetric Exclusion Processes on Lattices with Junctions

TL;DR

This paper develops an approximate mean-field theory and a correlation-aware domain-wall approach to analyze particle flow and phase behavior in asymmetric exclusion processes on lattices with junctions, validated by Monte Carlo simulations.

Contribution

It introduces a simple approximate theory and a modified domain-wall method to study complex junction lattice systems, extending understanding of phase transitions and correlations.

Findings

Three stationary phases identified depending on lattice branch states.

Theoretical predictions match Monte Carlo simulation results.

Correlation effects are crucial at phase boundaries.

Abstract

Totally asymmetric simple exclusion processes on lattices with junctions, where particles interact with hard-core exclusion and move on parallel lattice branches that at the junction combine into a single lattice segment, are investigated. A simple approximate theory, that treats the correlations around the junction position in a mean-field fashion, is developed in order to calculate stationary particle currents, density profiles and a phase diagram. It is shown that there are three possible stationary phases depending on the state of each of the lattice branch. At first-order phase boundaries, where the density correlations are important, a modified phenomenological domain-wall theory, that accounts for correlations, is introduced. Extensive Monte Carlo computer simulations are performed to investigate the system, and it is found that they are in excellent agreement with theoretical predictions.