Stirred Kardar-Parisi-Zhang equation with quenched random noise: Emergence of induced nonlinearity

Abstract

We study the stochastic Kardar-Parisi-Zhang equation for kinetic roughening where the time-independent (columnar or spatially quenched) Gaussian random noise $f(t,\mathbf{x})$ is specified by the pair correlation function $⟨f(t,\mathbf{x})f(t^{\prime },{\mathbf{x}}^{\prime })⟩\propto {\delta }^{(d)}(\mathbf{x}-{\mathbf{x}}^{\prime })$, $d$ being the dimension of space. The field-theoretic renormalization group analysis shows that the effect of turbulent motion of the environment (modelled by the coupling with the velocity field described by the Kazantsev-Kraichnan statistical ensemble for an incompressible fluid) gives rise to a new nonlinear term, quadratic in the velocity field. It turns out that this "induced" nonlinearity strongly affects the scaling behaviour in several universality classes (types of long-time, large-scale asymptotic regimes) even when the turbulent advection appears irrelevant in itself. Practical calculation of the critical exponents (that determine the universality classes) is performed to the first order of the double expansion in $\epsilon =4-d$ and the velocity exponent $\xi$ (one-loop approximation). As is the case with most "descendants" of the Kardar-Parisi-Zhang model, some relevant fixed points of the renormalization group equations lie in "forbidden zones," i.e. in those corresponding to negative kinetic coefficients or complex couplings. This persistent phenomenon in stochastic non-equilibrium models requires careful and inventive physical interpretation.

arXiv comment15 pages, 1 figure

References in corpus (54)

• Nonequilibrium Critical Phenomena and Phase Transitions into Absorbing States
• Particles and fields in fluid turbulence
• Colloquium: Criticality and dynamical scaling in living systems
• Controlled Collapse of a Bose-Einstein Condensate
• Applications of Field-Theoretic Renormalization Group Methods to Reaction-Diffusion Problems
• Power laws and Self-Organized Criticality in Theory and Nature
• An appetizer to modern developments on the Kardar-Parisi-Zhang universality class
• Non-perturbative renormalization group for the Kardar-Parisi-Zhang equation
• Critical Dynamics of the Contact Process with Quenched Disorder
• Renormalization Group, Operator Product Expansion, and Anomalous Scaling in a Model of Advected Passive Scalar
• Influence of compressibility on scaling regimes of strongly anisotropic fully developed turbulence
• Driven Diffusive Systems: An Introduction and Recent Developments
• Non-perturbative renormalisation group for the Kardar-Parisi-Zhang equation: general framework and first applications
• Upper critical dimension, dynamic exponent and scaling functions in the mode-coupling theory for the Kardar-Parisi-Zhang equation
• Width Distributions and the Upper Critical Dimension of KPZ Interfaces
• On the Perturbation Expansion of the KPZ-Equation
• On the Renormalization of the Kardar-Parisi-Zhang equation
• Quantized Scaling of Growing Surfaces
• Nonperturbative renormalization group for the stationary Kardar-Parisi-Zhang equation: scaling functions and amplitude ratios in 1+1, 2+1 and 3+1 dimensions
• Perturbative Field-Theoretical Renormalization Group Approach to Driven-Dissipative Bose-Einstein Criticality
• Non-perturbative renormalization of the KPZ growth dynamics
• Field Theory Approaches to Nonequilibrium Dynamics
• Universality of fluctuations in the Kardar-Parisi-Zhang class in high dimensions and its upper critical dimension
• Scalar transport in compressible flow
• Temporal coherence of one-dimensional non-equilibrium quantum fluids
• Localized growth modes, dynamic textures, and upper critical dimension for the Kardar-Parisi-Zhang equation in the weak noise limit
• The Kardar-Parisi-Zhang equation in the weak noise limit: Pattern formation and upper critical dimension
• Anisotropic Surface Growth Model in Disordered Media
• High dimensional behavior of the Kardar-Parisi-Zhang growth dynamics
• Effects of mixing and stirring on the critical behavior
• Effects of turbulent mixing on the nonequilibrium critical behaviour
• Existence of the upper critical dimension of the Kardar-Parisi-Zhang equation
• Scale invariance and dynamic phase transitions in diffusion-limited reactions
• Critical behaviour of a fluid in a random shear flow: Renormalization group analysis of a simplified model
• Langevin equations for reaction-diffusion processes
• Growth exponents of the etching model in high dimensions
• KPZ equation with short-range correlated noise: emergent symmetries and non-universal observables
• Kardar-Parisi-Zhang Equation with temporally correlated noise: a non-perturbative renormalization group approach
• Effects of turbulent transfer on the critical behaviour
• Non-universality in the erosion of tilted landscapes
• Accessing Kardar-Parisi-Zhang universality sub-classes with exciton polaritons
• Dynamics of Finger Formation in Laplacian Growth without Surface Tension
• Dynamic criticality far-from-equilibrium: one-loop flow of Burgers-Kardar-Parisi-Zhang systems with broken Galilean invariance
• Random interface growth in random environment: Renormalization group analysis of a simple model
• The Kardar-Parisi-Zhang model of a random kinetic growth: effects of a randomly moving medium
• Effects of Turbulent Environment and Random Noise on Self-Organized Critical Behavior: Universality vs Nonuniversality
• Static approach to renormalization group analysis of stochastic models with spatially quenched disorder
• Conserved Kardar-Parisi-Zhang equation: Role of quenched disorder in determining universality
• Patterns in the Kardar-Parisi-Zhang equation
• "Sinc"-Noise for the KPZ Equation
• Effects of turbulent environment on the surface roughening: The Kardar-Parisi-Zhang model coupled to the stochastic Navier-Stokes equation
• Kinetic roughening of the urban skyline
• Renormalization Group in the Problem of Active Scalar Advection
• Dynamic phase transitions in diffusion-limited reactions

Cited by in corpus (3)

• Disorders can induce continuously varying universal scaling in driven systems
• Field Theoretic Renormalization Group in an Infinite-Dimensional Model of Random Surface Growth in Random Environment
• Effect of random environment on kinetic roughening: Kardar-Parisi-Zhang model with a static noise coupled to the Navier-Stokes equation