Lane formation in a lattice model for oppositely driven binary particles

TL;DR

This paper studies how oppositely driven particles on a lattice form lanes or get stuck, using a combination of systematic steady state construction, mean-field analysis, and numerical simulations to understand phase behavior and finite size effects.

Contribution

It introduces a systematic method to construct steady states and uses mean-field analysis to estimate phase diagrams for lane formation in a lattice model.

Findings

Lane formations are well predicted by the mean-field analysis.

Finite size effects influence lane stability and formation.

Steady states include stuck configurations and dynamic lane patterns.

Abstract

Oppositely driven binary particles with repulsive interactions on the square lattice are investigated at the zero-temperature limit. Two classes of steady states related to stuck configurations and lane formations have been constructed in systematic ways under certain conditions. A mean-field type analysis carried out using a percolation problem based on the constructed steady states provides an estimation of the phase diagram, which is qualitatively consistent with numerical simulations. Further, finite size effects in terms of lane formations are discussed.