Surprising mappings of 2D polar active fluids to 2D soap and 1D sandblasting

TL;DR

This paper reveals a surprising universality class linking 2D polar active fluids, growing interfaces, smectic liquid crystals, and constrained ferromagnets, showing their shared non-equilibrium behavior and exact critical exponents.

Contribution

It uncovers a novel universality class connecting active fluids and interface growth, providing exact critical exponents and demonstrating robustness against fluctuations.

Findings

Incompressible polar active fluids in 2D belong to the same universality class as 1+1D KPZ interfaces.

Two-dimensional incompressible flocks exhibit universal long-range correlations.

Exact anisotropy and roughness exponents are determined for these systems.

Abstract

Active fluids and growing interfaces are two well-studied but very different non-equilibrium systems. Each exhibits non-equilibrium behavior quite different from that of their equilibrium counterparts. Here we demonstrate a surprising connection between these two: the ordered phase of incompressible polar active fluids in two spatial dimensions without momentum conservation, and growing one-dimensional interfaces (that is, the 1+1-dimensional Kardar-Parisi-Zhang equation), in fact belong to the same universality class. This universality class also includes two equilibrium systems : two-dimensional smectic liquid crystals, and a peculiar kind of constrained two-dimensional ferromagnet. We use these connections to show that two-dimensional incompressible flocks are robust against fluctuations, and exhibit universal long-ranged, anisotropic spatio-temporal correlations of those fluctuations. We also thereby determine the exact values of the anisotropy exponent $\zeta$ and the roughness exponents $\chi_{_{x,y}}$ that characterize these correlations.