Fluids of exciton-polaritons, excitations of two dimensional quantum wells in optical cavities, show collective phenomena akin to Bose condensation. However, a fundamental difference from standard condensates stems from the finite life-time of these excitations, which necessitate continuous driving to maintain a steady state. A basic question is whether a two dimensional condensate with long range algebraic correlations can exist under these non-equilibrium conditions. Here we show that such driven two-dimensional Bose systems cannot exhibit algebraic superfluid order except in low-symmetry, strongly anisotropic systems. Our result implies, in particular, that recent apparent evidence for Bose condensation of exciton-polaritons must be an intermediate scale crossover phenomenon, while the true long distance correlations fall off exponentially. We obtain these results through a mapping of the long-wavelength condensate dynamics onto the anisotropic Kardar-Parisi-Zhang equation.arXiv:1311.0876v2 [cond-mat.stat-mech]

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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.

We study incompressible systems of motile particles with alignment interactions. Unlike their compressible counterparts, in which the order-disorder (i.e., moving to static) transition, tuned by either noise or number density, is discontinuous, in incompressible systems this transition can be continuous, and belongs to a new universality class. We calculate the critical exponents to ϵ  ( )in an ϵ = − d 4 expansion, and derive two exact scaling relations. This is the first analytic treatment of a phase transition in a new universality class in an active system. OPEN ACCESS RECEIVED

We study universal behavior in the moving (polar ordered) phase of a generic system of motile particles with alignment interactions in the incompressible limit for spatial dimensions d>2. Using a dynamical renormalization group analysis, we obtain the exact dynamic, roughness, and anisotropy exponents that describe the scaling behavior of such incompressible systems. This is the first time a compelling argument has been given for the exact values of the anomalous scaling exponents of a flock moving through an isotropic medium in d>2. We note, however, that these exponents are not continuous at d=2; that is, the exponents do not take on the values given by equations (2) in d=2 [12]. This is because, as we will show in this paper, and as also discussed in [12], the number of soft modes in incompressible flocks is d−2. Because this vanishes in d=2, the 2D case is special, and is not characterized by the exponents (2).Results identical to (2) have been conjectured for compressible polar active fluids [2, 4] and Malthusian flocks [15], but only in the latter case, and even there only in 2D, can a compelling argument for them be made. The results we present here make incompressible flocks the first polar active system with underlying isotropic symmetry in d>2 for which the exact scaling laws have been determined.