Phenomenology of ageing in the Kardar-Parisi-Zhang equation

Abstract

We study ageing during surface growth processes described by the one-dimensional Kardar-Parisi-Zhang equation. Starting from a flat initial state, the systems undergo simple ageing in both correlators and linear responses and its dynamical scaling is characterised by the ageing exponents a=-1/3, b=-2/3, lambda_C=lambda_R=1 and z=3/2. The form of the autoresponse scaling function is well described by the recently constructed logarithmic extension of local scale-invariance.

Latex2e, 5 pages, with 4 figures, final form

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Cited by in corpus (39)

• Anomalous diffusion: A basic mechanism for the evolution of inhomogeneous systems
• Evidence for geometry-dependent universal fluctuations of the Kardar-Parisi-Zhang interfaces in liquid-crystal turbulence
• Universal correlators and distributions as experimental signatures of 2+1 Kardar-Parisi-Zhang growth
• The effect of the Magnus force on skyrmion relaxation dynamics
• Aging in the long-range Ising model
• Phase Transitions and Scaling in Systems Far From Equilibrium
• Memory and universality in interface growth
• Field-Theoretic Thermodynamic Uncertainty Relation -- General formulation exemplified with the Kardar-Parisi-Zhang equation
• Ageing of the 2+1 dimensional Kardar-Parisi-Zhang model
• Spherical model of growing interfaces
• Tail of the two-time height distribution for KPZ growth in one dimension
• Dynamical symmetries and causality in non-equilibrium phase transitions
• Schrödinger symmetry: a historical review
• Aging processes in systems with anomalous slow dynamics
• From dynamical scaling to local scale-invariance: a tutorial
• Dynamical universality classes of simple growth and lattice gas models
• Causality from dynamical symmetry: an example from local scale-invariance
• Clustering, intermittency and scaling for passive particles on fluctuating surfaces
• Dynamical universality of the contact process
• Non-local meta-conformal invariance, diffusion-limited erosion and the XXZ chain
• Comparison of Different Parallel Implementations of the 2+1-Dimensional KPZ Model and the 3-Dimensional KMC Model
• Non-local representations of the ageing algebra in higher dimensions
• Logarithmic Exotic Conformal Galilean Algebras
• Local Scale-Invariance of the 2+1 dimensional Kardar-Parisi-Zhang model
• Aging Logarithmic Conformal Field Theory : a holographic view
• Physical ageing and new representations of some Lie algebras of local scale-invariance
• Logarithmic correlators or responses in non-relativistic analogues of conformal invariance
• Physical ageing from generalised time-translation-invariance
• KPZ fluctuations in finite volume
• Critical initial-slip scaling for the noisy complex Ginzburg-Landau equation
• Exactly solvable models of growing interfaces and lattice gases: the Arcetri models, ageing and logarithmic sub-ageing
• Invited review: KPZ. Recent developments via a variational formulation
• Relaxation after a change in the interface growth dynamics
• Non-local meta-conformal invariance in diffusion-limited erosion
• Time evolution of intermittency in the passive slider problem
• Aging Logarithmic Galilean Field Theories
• One-point height fluctuations and two-point correlators of $(2+1)$ cylindrical KPZ systems
• Boundary crossover in non-equilibrium growth processes
• Fractional Galilean Symmetries