Novel universality classes of coupled driven diffusive systems

Logarithmic or algebraic: Roughening of an active Kardar-Parisi-Zhang surface

The Kardar-Parisi-Zhang (KPZ) equation sets the universality class for growing and roughening of nonequilibrium surfaces without any conservation law and nonlocal effects. We argue here that the KPZ equation can be generalized by including a symmetry-permitted nonlocal nonlinear term of active origin that is of the same order as the one included in the KPZ equation. Including this term, the 2D active KPZ equation is stable in some parameter regimes, in which the interface conformation fluctuations exhibit sublogarithmic or superlogarithmic roughness, with nonuniversal exponents, giving positional generalized quasi-long-ranged order. For other parameter choices, the model is unstable, suggesting a perturbatively inaccessible algebraically rough interface or positional short-ranged order. Our model should serve as a paradigmatic nonlocal growth equation.

Mobility-induced order in active XY spins on a substrate

We elucidate that the nearly phase-ordered active XY spins in contact with a conserved, diffusing species on a substrate can be stable. For wide-ranging model parameters, it has stable uniform phases robust against noises. These are distinguished by generalized quasi-long-range (QLRO) orientational order logarithmically stronger or weaker than the well-known QLRO in equilibrium, together with miniscule (i.e., hyperuniform) or giant number fluctuations, respectively. This illustrates a direct correspondence between the two. The scaling of both phase and density fluctuations in the stable phase-ordered states is nonuniversal: they depend on the nonlinear dynamical couplings. For other parameters, it has no stable uniformly ordered phase. Our model, a theory for active spinners, provides a minimal framework for wide-ranging systems, e.g., active superfluids on substrates, synchronization of oscillators, active carpets of cilia and bacterial flagella, and active membranes.

Active XY model on a substrate: Density fluctuations and phase ordering

We explore the generic long-wavelength properties of an active XY model on a substrate, consisting of a collection of nearly phase-ordered active XY spins in contact with a diffusing, conserved species, as a representative system of active spinners with a conservation law. The spins rotate actively in response to the local density fluctuations and local phase differences, on a solid substrate. We investigate this system by Monte Carlo simulations of an agent-based model, which we set up, complemented by the hydrodynamic theory for the system. We demonstrate that this system can phase-synchronize without any hydrodynamic interactions. Our combined numerical and analytical studies show that this model, when stable, displays hitherto unstudied scaling behavior: As a consequence of the interplay between the mobility, active rotation, and number conservation, such a system can be stable over a wide range of the model parameters characterized by a novel correspondence between the phase and density fluctuations. In different regions of the phase space where the phase-ordered system is stable, it displays generalized quasi-long-range order (QLRO): It shows phase ordering which is generically either logarithmically stronger than the conventional QLRO found in its equilibrium limit, together with "miniscule number fluctuations," or logarithmically weaker than QLRO along with "giant number fluctuations," showing a novel one-to-one correspondence between phase ordering and density fluctuations in the ordered states. Intriguingly, these scaling exponents are found to depend explicitly on the model parameters. We further show that in other parameter regimes there are no stable, ordered phases. Instead, two distinct types of disordered states with short-range phase order are found, characterized by the presence or absence of stable clusters of finite sizes. In a surprising connection, the hydrodynamic theory for this model also describes the fluctuations in a Kardar-Parisi-Zhang (KPZ) surface with a conserved species on it, or an active fluid membrane with a finite tension, without momentum conservation and a conserved species living on it. This implies the existence of stable fluctuating surfaces that are only logarithmically smoother or rougher than the Edward-Wilkinson surface at two dimensions (2D) can exist, in contrast to the 2D pure KPZ-like "rough" surfaces.

Noise cross correlations can induce instabilities in coupled driven models

We study the effects of noise cross correlations on the steady states of driven, nonequilibrium systems, which are described by two stochastically driven dynamical variables, in one dimension. We use a well-known stochastically driven coupled model with two dynamical variables, where one of the variables is autonomous, being independent of the other, whereas the second one depends explicitly on the former. Introducing cross correlations of the two noises in the two dynamical equations, we show that depending upon the details of the nonlinear coupling between the dynamical fields, such cross correlations can induce instabilities in the models that are otherwise stable in the absence of any cross correlations. We argue that this is reminiscent of the roughening transition found in the Kardar-Parisi-Zhang equation in dimensions greater than two. Phenomenological implications of our results are discussed.

Rough or crumpled: Phases in kinetic growth with surface relaxation

We show that generic kinetic growth processes with surface relaxations can exhibit a hitherto unexplored crumpled phase with short-range orientational order at dimensions d<4. A sufficiently strong spatially nonlocal part of the chemical potential associated with the particle current above a threshold in the system can trigger this crumpling. The system can also be in a perturbatively accessible rough phase with long-range orientational order but short-range positional order at d<4 with known scaling exponents. Intriguingly, in d>4 we argue that there is no crumpling transition; instead, there is a roughening transition from a smooth to a rough phase for large enough nonlocal particle chemical potential. Experimental and theoretical implications of these results are discussed.

Disorders can induce continuously varying universal scaling in driven systems

We elucidate the nature of universal scaling in a class of quenched disordered driven models. In particular, we explore the intriguing possibility of whether coupling with quenched disorders can lead to continuously varying universality classes. We examine this question in the context of the Kardar-Parisi-Zhang (KPZ) equation, with and without a conservation law, coupled with quenched disorders having distributions with pertinent structures. We show that when the disorder is relevant in the renormalization group sense, the scaling exponents can depend continuously on a dimensionless parameter that defines the disorder distribution. This result is generic and holds for quenched disorders with or without spatially long-ranged correlations, as long as the disorder remains a "relevant perturbation" on the pure system in the renormalization group sense and a dimensionless parameter naturally exists in its distribution. We speculate on its implications for generic driven systems with quenched disorders, and we compare and contrast with the scaling displayed in the presence of annealed disorders.

Continuous universality in nonequilibrium relaxational dynamics of O2 symmetric systems

We elucidate a nonconserved relaxational nonequilibrium dynamics of a O(2) symmetric model. We drive the system out of equilibrium by introducing a nonzero noise cross correlation of amplitude D(×) in a stochastic Langevin description of the system, while maintaining the O(2) symmetry of the order parameter space. By performing dynamic renormalization group calculations in a field-theoretic set up, we analyze the ensuing nonequilibrium steady states and evaluate the scaling exponents near the critical point, which now depend explicitly on D(×). Since the latter remains unrenormalized, we obtain universality classes varying continuously with D(×). More interestingly, by changing D(×) continuously from zero, we can make our system move away from its equilibrium behavior (i.e., when D(×)=0) continuously and incrementally.