Origin of Edge Currents in Chiral Active Liquids

TL;DR

This paper explains the origin of unidirectional edge currents in chiral active liquids as a consequence of global angular momentum conservation, deriving an Ohmic conductance law and validating it through simulations.

Contribution

It introduces a microscopic explanation for edge currents in chiral active liquids based on angular momentum conservation, with derived laws and validated numerical results.

Findings

Edge currents arise from angular momentum conservation.

Derived an Ohmic-like conductance law for edge currents.

Validated results with molecular dynamics simulations.

Abstract

Chiral active liquids exhibit unidirectional edge currents when confined to simple geometries, but the origin of this phenomenon has defied explanation. Starting from the microscopic equations of motion of a simple two-dimensional model, we find that localized edge currents emerge as a consequence of global angular momentum conservation in dense systems. From these underlying equations, we derive an Ohmic-like conductance law for the mean edge current in the dense phase, and we find it to be intensive, depending only on the density, active torque and substrate drag. For simple geometries, we find the distribution of the edge currents has a closed Gaussian form, with a variance that is intensive, depending only on temperature, density and the aspect ratio of the system. These results are validated numerically using extensive molecular dynamics simulations. These results provide a new perspective for studying the collective phenomena in active matter through the global balance of conserved quantities.