Dynamic criticality far-from-equilibrium: one-loop flow of Burgers-Kardar-Parisi-Zhang systems with broken Galilean invariance

Burgers-Kardar-Parisi-Zhang (KPZ) scaling has recently (re-) surfaced in a variety of physical contexts, ranging from anharmonic chains to quantum systems such as open superfluids, in which a variety of random forces may be encountered and/or engineered. Motivated by these developments, we here provide a generalization of the KPZ universality class to situations with long-ranged temporal correlations in the noise, which purposefully break the Galilean invariance that is central to the conventional KPZ solution. We compute the phase diagram and critical exponents of the KPZ equation with $1/f$-noise (KPZ$_{1/f}$) in spatial dimensions $1\leq d < 4$ using the dynamic renormalization group with a frequency cutoff technique in a one-loop truncation. Distinct features of KPZ$_{1/f}$ are: (i) a generically scale-invariant, rough phase at high noise levels that violates fluctuation-dissipation relations and exhibits hyperthermal statistics {\it even in d=1}, (ii) a fine-tuned roughening transition at which the flow fulfills an emergent thermal-like fluctuation-dissipation relation, that separates the rough phase from (iii) a {\it massive phase} in $1< d < 4$ (in $d=1$ the interface is always rough). We point out potential connections to nonlinear hydrodynamics with a reduced set of conservation laws and noisy quantum liquids.Comment: 29 pages, 11 figures, 1 table, 54 references, v2 as publishe

Quantum macrostatistical picture of nonequilibrium steady states

We employ a quantum macrostatistical treatment of irreversible processes to prove that, in nonequilibrium steady states, (a) the hydrodynamical observables execute a generalised Onsager-Machlup process and (b) the spatial correlations of these observables are generically of long range. The key assumptions behind these results are a nonequilibrium version of Onsager's regression hypothesis, together with certain hypotheses of chaoticity and local equilibrium for hydrodynamical fluctuations.Comment: TeX, 13 page

Perturbative Field-Theoretical Renormalization Group Approach to Driven-Dissipative Bose-Einstein Criticality

The universal critical behavior of the driven-dissipative non-equilibrium Bose-Einstein condensation transition is investigated employing the field-theoretical renormalization group method. Such criticality may be realized in broad ranges of driven open systems on the interface of quantum optics and many-body physics, from exciton-polariton condensates to cold atomic gases. The starting point is a noisy and dissipative Gross-Pitaevski equation corresponding to a complex valued Landau-Ginzburg functional, which captures the near critical non-equilibrium dynamics, and generalizes Model A for classical relaxational dynamics with non-conserved order parameter. We confirm and further develop the physical picture previously established by means of a functional renormalization group study of this system. Complementing this earlier numerical analysis, we analytically compute the static and dynamical critical exponents at the condensation transition to lowest non-trivial order in the dimensional epsilon expansion about the upper critical dimension d_c = 4, and establish the emergence of a novel universal scaling exponent associated with the non-equilibrium drive. We also discuss the corresponding situation for a conserved order parameter field, i.e., (sub-)diffusive Model B with complex coefficients.Comment: 17 pages, 6 figures, to appear in Phys. Rev. X (2014

The low noise phase of a 2d active nematic

We consider a collection of self-driven apolar particles on a substrate that organize into an active nematic phase at sufficiently high density or low noise. Using the dynamical renormalization group, we systematically study the 2d fluctuating ordered phase in a coarse-grained hydrodynamic description involving both the nematic director and the conserved density field. In the presence of noise, we show that the system always displays only quasi-long ranged orientational order beyond a crossover scale. A careful analysis of the nonlinearities permitted by symmetry reveals that activity is dangerously irrelevant over the linearized description, allowing giant number fluctuations to persist though now with strong finite-size effects and a non-universal scaling exponent. Nonlinear effects from the active currents lead to power law correlations in the density field thereby preventing macroscopic phase separation in the thermodynamic limit.Comment: 17 pages, 5 figure

Stochastic Porous Media Equation and Self-Organized Criticality

The existence and uniqueness of nonnegative strong solutions for stochastic porous media equations with noncoercive monotone diffusivity function and Wiener forcing term is proven. The finite time extinction of solutions with high probability is also proven in 1-D. The results are relevant for self-organized critical behaviour of stochastic nonlinear diffusion equations with critical states.Comment: 29 pages, BiBoS-Preprint No. 07-11-26

Universality classes in nonequilibrium lattice systems

This work is designed to overview our present knowledge about universality classes occurring in nonequilibrium systems defined on regular lattices. In the first section I summarize the most important critical exponents, relations and the field theoretical formalism used in the text. In the second section I briefly address the question of scaling behavior at first order phase transitions. In section three I review dynamical extensions of basic static classes, show the effect of mixing dynamics and the percolation behavior. The main body of this work is given in section four where genuine, dynamical universality classes specific to nonequilibrium systems are introduced. In section five I continue overviewing such nonequilibrium classes but in coupled, multi-component systems. Most of the known nonequilibrium transition classes are explored in low dimensions between active and absorbing states of reaction-diffusion type of systems. However by mapping they can be related to universal behavior of interface growth models, which I overview in section six. Finally in section seven I summarize families of absorbing state system classes, mean-field classes and give an outlook for further directions of research.Comment: Updated comprehensive review, 62 pages (two column), 29 figs included. Scheduled for publication in Reviews of Modern Physics in April 200

Keldysh Field Theory for Driven Open Quantum Systems

Recent experimental developments in diverse areas - ranging from cold atomic gases over light-driven semiconductors to microcavity arrays - move systems into the focus, which are located on the interface of quantum optics, many-body physics and statistical mechanics. They share in common that coherent and driven-dissipative quantum dynamics occur on an equal footing, creating genuine non-equilibrium scenarios without immediate counterpart in condensed matter. This concerns both their non-thermal flux equilibrium states, as well as their many-body time evolution. It is a challenge to theory to identify novel instances of universal emergent macroscopic phenomena, which are tied unambiguously and in an observable way to the microscopic drive conditions. In this review, we discuss some recent results in this direction. Moreover, we provide a systematic introduction to the open system Keldysh functional integral approach, which is the proper technical tool to accomplish a merger of quantum optics and many-body physics, and leverages the power of modern quantum field theory to driven open quantum systems.Comment: 73 pages, 13 figure

Non-local response in a lattice gas under a shear drive

In equilibrium, the effect of a spatially localised perturbation is typically confined around the perturbed region. Quite contrary to this, in a non-equilibrium stationary state often the entire system is affected. This appears to be a generic feature of non-equilibrium. We study such non-local response in the stationary state of a lattice gas with a shear drive at the boundary which keeps the system out of equilibrium. We show that a perturbation in the form of a localised blockage at the boundary, induces algebraically decaying density and current profile. In two examples, non-interacting particles and particles with simple exclusion, we analytically derive the power-law tail of the profiles.Comment: 32 pages, 7 figure

Non-equilibrium fixed points of coupled Ising models

Driven-dissipative systems are expected to give rise to non-equilibrium phenomena that are absent in their equilibrium counterparts. However, phase transitions in these systems generically exhibit an effectively classical equilibrium behavior in spite of their non-equilibrium origin. In this paper, we show that multicritical points in such systems lead to a rich and genuinely non-equilibrium behavior. Specifically, we investigate a driven-dissipative model of interacting bosons that possesses two distinct phase transitions: one from a high- to a low-density phase---reminiscent of a liquid-gas transition---and another to an antiferromagnetic phase. Each phase transition is described by the Ising universality class characterized by an (emergent or microscopic) $\mathbb{Z}_2$ symmetry. They, however, coalesce at a multicritical point, giving rise to a non-equilibrium model of coupled Ising-like order parameters described by a $\mathbb{Z}_2 \times \mathbb{Z}_2$ symmetry. Using a dynamical renormalization-group approach, we show that a pair of non-equilibrium fixed points (NEFPs) emerge that govern the long-distance critical behavior of the system. We elucidate various exotic features of these NEFPs. In particular, we show that a generic continuous scale invariance at criticality is reduced to a discrete scale invariance. This further results in complex-valued critical exponents and spiraling phase boundaries, and it is also accompanied by a complex Liouvillian gap even close to the phase transition. As direct evidence of the non-equilibrium nature of the NEFPs, we show that the fluctuation-dissipation relation is violated at all scales, leading to an effective temperature that becomes "hotter" and "hotter" at longer and longer wavelengths. Finally, we argue that this non-equilibrium behavior can be observed in cavity arrays with cross-Kerr nonlinearities.Comment: 19+11 pages, 7+9 figure