Universal Long Ranged Correlations in Driven Binary Mixtures

TL;DR

This paper investigates the pair correlations in driven binary mixtures, revealing universal long-range algebraic decay along the motion direction and exponential decay transversely, confirmed by simulations.

Contribution

It provides an analytical framework for understanding correlations in dense driven mixtures, demonstrating their universal long-range behavior.

Findings

Correlations decay algebraically along the direction of motion.

Correlations have a self-similar exponential profile transversely.

Simulation results confirm the analytical predictions beyond the theory's validity.

Abstract

When two populations of "particles" move in opposite directions, like oppositely charged colloids under an electric field or intersecting flows of pedestrians, they can move collectively, forming lanes along their direction of motion. The nature of this "laning transition" is still being debated and, in particular, the pair correlation functions, which are the key observables to quantify this phenomenon, have not been characterized yet. Here, we determine the correlations using an analytical approach based on a linearization of the stochastic equations for the density fields, which is valid for dense systems of soft particles. We find that the correlations decay algebraically along the direction of motion, and have a self-similar exponential profile in the transverse direction. Brownian dynamics simulations confirm our theoretical predictions and show that they also hold beyond the validity range of our analytical approach, pointing to a universal behavior.