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.

6 Pages, 5 Figures

References in corpus (11)

• Probability Distribution of the Free Energy of the Continuum Directed Random Polymer in 1+1 dimensions
• Growing interfaces uncover universal fluctuations behind scale invariance
• Exact scaling functions for one-dimensional stationary KPZ growth
• An exact solution for the KPZ equation with flat initial conditions
• Evidence for geometry-dependent universal fluctuations of the Kardar-Parisi-Zhang interfaces in liquid-crystal turbulence
• The KPZ equation with flat initial condition and the directed polymer with one free end
• Kardar-Parisi-Zhang universality class in 2+1 dimensions: Universal geometry-dependent distributions and finite-time corrections
• Statistics of circular interface fluctuations in an off-lattice Eden model
• Slow relaxation and aging kinetics for the driven lattice gas
• Distribution of extremes in the fluctuations of two-dimensional equilibrium interfaces
• Maximal and minimal height distributions of fluctuating interfaces

Cited by in corpus (25)

• Universality of fluctuations in the Kardar-Parisi-Zhang class in high dimensions and its upper critical dimension
• 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
• 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
• Spreading fronts of wetting liquid droplets: microscopic simulations and universal fluctuations
• Local average height distribution of fluctuating interfaces
• Non-local meta-conformal invariance, diffusion-limited erosion and the XXZ chain
• Melting of an Ising Quadrant
• Local Scale-Invariance of the 2+1 dimensional Kardar-Parisi-Zhang model
• Exactly solvable models of growing interfaces and lattice gases: the Arcetri models, ageing and logarithmic sub-ageing
• KPZ modes in $d$-dimensional directed polymers
• 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
• Height distributions in interface growth: The role of the averaging process
• Dimensional crossover in Kardar-Parisi-Zhang growth
• Steady-state skewness and kurtosis from renormalized cumulants in $(2+1)$-dimensional stochastic surface growth
• Universal interface fluctuations in the contact process
• Nonconserved critical dynamics of the two-dimensional Ising model as a surface kinetic roughening process
• Exponents and front fluctuations in the quenched Kardar-Parisi-Zhang universality class of one- and two- dimensional interfaces