title: Mapping two-dimensional polar active fluids to two-dimensional soap and one-dimensional sandblasting.
abstract: Active fluids and growing interfaces are two well-studied but very different non-equilibrium systems. Each exhibits non-equilibrium behaviour distinct 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 ζ and the roughness exponents χx,y that characterize these correlations.
authors.affiliation: Department of Physics, College of Science, China University of Mining and Technology, Xuzhou, Jiangsu 221116, China.
authors.forename: Leiming
authors.initials: L
authors.lastname: Chen
authors.affiliation: Department of Bioengineering, Imperial College London, South Kensington Campus, London SW7 2AZ, UK.
authors.forename: Chiu Fan
authors.initials: CF
authors.lastname: Lee
authors.affiliation: Department of Physics and Institute of Theoretical Science, University of Oregon, Eugene, Oregon 97403, USA.|Max Planck Institute for the Physics of Complex Systems, Nöthnitzer Strasse 38, 01187 Dresden, Germany.
authors.forename: John
authors.initials: J
authors.lastname: Toner