Universal correlators and distributions as experimental signatures of 2+1 Kardar-Parisi-Zhang growth

Abstract

We examine height-height correlations in the transient growth regime of the 2+1 Kardar-Parisi-Zhang (KPZ) universality class, with a particular focus on the {\it spatial covariance} of the underlying two-point statistics, higher-dimensional analog of the 1+1 KPZ Class Airy${}_1$ process. Making comparison to AFM kinetic roughening data in 2d organic thin films, we use our universal 2+1 KPZ spatial covariance to extract key scaling parameters for this experimental system. Additionally, we explore the i) height, ii) local roughness, and iii) extreme value distributions characteristic of these oligomer films, finding compelling agreement in all instances with our numerical integration of the KPZ equation itself. Finally, investigating nonequilibrium relaxation phenomena exhibited by 2+1 KPZ Class models, we have unearthed a universal KPZ ageing kinetics. In experiments with ample data in the time domain, our 2+1 KPZ Euler {\it temporal covariance} will allow a quick, independent estimate of the central KPZ scaling parameter.

arXiv comment6 Pages, 5 Figures

References in corpus (39)

• Stochastic thermodynamics, fluctuation theorems, and molecular machines
• Level-Spacing Distributions and the Airy Kernel
• Shape Fluctuations and Random Matrices
• On Orthogonal and Symplectic Matrix Ensembles
• Probability Distribution of the Free Energy of the Continuum Directed Random Polymer in 1+1 dimensions
• Universal Distributions for Growth Processes in 1+1 Dimensions and Random Matrices
• The one-dimensional KPZ equation: an exact solution and its universality
• Universal Fluctuations of Growing Interfaces: Evidence in Turbulent Liquid Crystals
• Free-energy distribution of the directed polymer at high temperature
• Growing interfaces uncover universal fluctuations behind scale invariance
• Exact scaling functions for one-dimensional stationary KPZ growth
• Bethe anzats derivation of the Tracy-Widom distribution for one-dimensional directed polymers
• An exact solution for the KPZ equation with flat initial conditions
• Airy Distribution Function: From the Area Under a Brownian Excursion to the Maximal Height of Fluctuating Interfaces
• Exact Maximal Height Distribution of Fluctuating Interfaces
• Evidence for geometry-dependent universal fluctuations of the Kardar-Parisi-Zhang interfaces in liquid-crystal turbulence
• Exact solution for the stationary Kardar-Parisi-Zhang equation
• Critical Exponents of the KPZ Equation via Multi-Surface Coding Numerical Simulations
• The KPZ equation with flat initial condition and the directed polymer with one free end
• Maximal Height Scaling of Kinetically Growing Surfaces
• Stationary correlations for the 1D KPZ equation
• Extremely large scale simulation of a Kardar-Parisi-Zhang model using graphics cards
• Universal fluctuations in the growth of semiconductor thin films
• Roughness distributions for 1/f^alpha signals
• Persistence of Kardar-Parisi-Zhang Interfaces
• Kardar-Parisi-Zhang universality class in 2+1 dimensions: Universal geometry-dependent distributions and finite-time corrections
• Universal Asymptotic Statistics of Maximal Relative Height in One-dimensional Solid-on-solid Models
• Crossover from Growing to Stationary Interfaces in the Kardar-Parisi-Zhang Class
• Extremal statistics of curved growing interfaces in 1+1 dimensions
• Universal aspects of curved, flat & stationary-state Kardar-Parisi-Zhang statistics
• Universal fluctuations in radial growth models belonging to the KPZ universality class
• Phenomenology of ageing in the Kardar-Parisi-Zhang equation
• Statistics of circular interface fluctuations in an off-lattice Eden model
• Universal fluctuations in KPZ growth on one-dimensional flat substrates
• Slow relaxation and aging kinetics for the driven lattice gas
• Short-time scaling behavior of growing interfaces
• Height and roughness distributions in thin films with Kardar-Parisi-Zhang scaling
• Distribution of extremes in the fluctuations of two-dimensional equilibrium interfaces
• Maximal and minimal height distributions of fluctuating interfaces

Cited by in corpus (50)

• Keldysh Field Theory for Driven Open Quantum Systems
• A KPZ Cocktail- Shaken, not stirred: Toasting 30 years of kinetically roughened surfaces
• An appetizer to modern developments on the Kardar-Parisi-Zhang universality class
• Dynamical critical exponents in driven-dissipative quantum systems
• Universality of fluctuations in the Kardar-Parisi-Zhang class in high dimensions and its upper critical dimension
• Tuning across Universalities with a Driven Open Condensate
• Universality and dependence on initial conditions in the class of the nonlinear molecular beam epitaxy equation
• Interface fluctuations for deposition on enlarging flat substrates
• Initial pseudo-steady state & asymptotic KPZ universality in semiconductor on polymer deposition
• Temperature effect on (2+1) experimental Kardar-Parisi-Zhang growth
• Diffusion in time-dependent random media and the Kardar-Parisi-Zhang equation
• Spatial and Temporal Coherence in Strongly Coupled Plasmonic Bose-Einstein Condensates
• KPZ equation with short-range correlated noise: emergent symmetries and non-universal observables
• Substrate effects and diffusion dominated roughening in Cu2O electrodeposition
• Ageing of the 2+1 dimensional Kardar-Parisi-Zhang model
• Spherical model of growing interfaces
• From dynamical scaling to local scale-invariance: a tutorial
• Geometry dependence in linear interface growth
• Dynamical universality classes of simple growth and lattice gas models
• Emergent Kardar-Parisi-Zhang phase in quadratically driven condensates
• Surface coupling effects on the capacitance of thin insulating films
• Kardar-Parisi-Zhang universality class in ($d+1$)-dimensions
• Searching for the Kardar-Parisi-Zhang phase in microcavity polaritons
• Hallmarks of the Kardar-Parisi-Zhang universality class elicited by scanning probe microscopy
• Spreading fronts of wetting liquid droplets: microscopic simulations and universal fluctuations
• Non-local meta-conformal invariance, diffusion-limited erosion and the XXZ chain
• Local average height distribution of fluctuating interfaces
• Scaling of local roughness distributions
• Melting of an Ising Quadrant
• Local Scale-Invariance of the 2+1 dimensional Kardar-Parisi-Zhang model
• Width and extremal height distributions of fluctuating interfaces with window boundary conditions
• Stochastic heat equation limit of a (2+1)d growth model
• Height fluctuations in homoepitaxial thin film growth: A numerical study
• Exactly solvable models of growing interfaces and lattice gases: the Arcetri models, ageing and logarithmic sub-ageing
• Critical initial-slip scaling for the noisy complex Ginzburg-Landau equation
• Radial Restricted Solid-on-Solid and Etching Interface Growth Models
• KPZ modes in $d$-dimensional directed polymers
• Non-local meta-conformal invariance in diffusion-limited erosion
• Two-dimensional Anisotropic KPZ growth and limit shapes
• Finite-size corrections to scaling of the magnetization distribution in the $2d$ $XY$-model at zero temperature
• Phase diagram and universal scaling regimes of two-dimensional exciton-polariton Bose-Einstein condensates
• One-point height fluctuations and two-point correlators of $(2+1)$ cylindrical KPZ systems
• Bit-Vectorized GPU Implementation of a Stochastic Cellular Automaton Model for Surface Growth
• Numerical calculation of overlap distribution of $(2+1)$-dimensional directed polymer in random media
• Nonconserved critical dynamics of the two-dimensional Ising model as a surface kinetic roughening process
• Dimensional crossover in Kardar-Parisi-Zhang growth
• Height distributions in interface growth: The role of the averaging process
• Steady-state skewness and kurtosis from renormalized cumulants in $(2+1)$-dimensional stochastic surface growth
• Universal interface fluctuations in the contact process
• Exponents and front fluctuations in the quenched Kardar-Parisi-Zhang universality class of one- and two- dimensional interfaces