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Related papers: Local KPZ behavior under arbitrary scaling limits

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We study height and roughness distributions of films grown with discrete Kardar-Parisi-Zhang (KPZ) models in a small time regime which is expected to parallel the typical experimental conditions. Those distributions are measured with square…

Statistical Mechanics · Physics 2015-06-25 Thereza Paiva , F. D. A. Aarao Reis

We present an exact solution of the {\it deterministic} Kardar-Parisi-Zhang (KPZ) equation under the influence of a local driving force $f$. For substrate dimension $d \le 2$ we recover the well-known result that for arbitrarily small…

Condensed Matter · Physics 2009-10-28 T. J. Newman , Harald Kallabis

We study the simple, linear, Edwards-Wilkinson equation that describes surface growth governed by height diffusion in the presence of spatiotemporally power-law decaying correlated noise. We analytically show that the surface becomes…

Pattern Formation and Solitons · Physics 2020-04-22 Alejandro Alés , Juan M López

This article reviews recent developments in statistical field theory far from equilibrium. It focuses on the Kardar-Parisi-Zhang equation of stochastic surface growth and its mathematical relatives, namely the stochastic Burgers equation in…

Condensed Matter · Physics 2015-06-25 Michael Lassig

We provide a comprehensive report on scale-invariant fluctuations of growing interfaces in liquid-crystal turbulence, for which we recently found evidence that they belong to the Kardar-Parisi-Zhang (KPZ) universality class for 1+1…

Statistical Mechanics · Physics 2012-06-25 Kazumasa A. Takeuchi , Masaki Sano

Recently, a variational approach has been introduced for the paradigmatic Kardar--Parisi--Zhang (KPZ) equation. Here we review that approach, together with the functional Taylor expansion that the KPZ nonequilibrium potential (NEP) admits.…

Statistical Mechanics · Physics 2014-01-27 Horacio S. Wio , Roberto R. Deza , Carlos Escudero , Jorge A. Revelli

The effects of spatially correlated noise on a phenomenological equation equivalent to a non-local version of the Kardar-Parisi-Zhang equation are studied via the dynamic renormalization group (DRG) techniques. The correlated noise coupled…

Statistical Mechanics · Physics 2009-10-31 Amit Kr. Chattopadhyay

We study the atypically large deviations of the height $H \sim {{\cal O}}(t)$ at the origin at late times in $1+1$-dimensional growth models belonging to the Kardar-Parisi-Zhang (KPZ) universality class. We present exact results for the…

Statistical Mechanics · Physics 2016-05-04 Pierre Le Doussal , Satya N. Majumdar , Gregory Schehr

To investigate universal behavior and effects of long-range temporal correlations in kinetic roughening, we perform extensive simulations on the Kardar-Parisi-Zhang (KPZ) equation with temporally correlated noise based on pseudospectral…

Statistical Mechanics · Physics 2023-04-18 Xiongpeng Hu , Dapeng Hao , Hui Xia

A modified Kardar-Parisi-Zhang (KPZ) equation is introduced, and solved exactly in the infinite-range limit. In the low-noise limit the system exhibits a weak-to-strong coupling transition, rounded for non-zero noise, as a function of the…

Condensed Matter · Physics 2009-10-28 M. Marsili , A. J. Bray

The Kardar-Parisi-Zhang (KPZ) equation is a stochastic partial differential equation which is ill-posed because the nonlinearity is marginally defined with respect to the roughness of the forcing noise. However, its Cole-Hopf solution,…

Probability · Mathematics 2014-07-29 Tadahisa Funaki , Jeremy Quastel

We simulate competitive two-component growth on a one dimensional substrate of $L$ sites. One component is a Poisson-type deposition that generates Kardar-Parisi-Zhang (KPZ) correlations. The other is random deposition (RD). We derive the…

Materials Science · Physics 2009-02-01 A. Kolakowska , M. A. Novotny , P. S. Verma

We study Kardar-Parisi-Zhang equation in spatial dimension 3 or larger driven by a Gaussian space-time white noise with a small convolution in space. When the noise intensity is small, it is known that the solutions converge to a random…

Probability · Mathematics 2020-05-20 Francis Comets , Clement Cosco , Chiranjib Mukherjee

We provide a detailed Dynamic Renormalization Group study for a class of stochastic equations that describe non-conserved interface growth mediated by non-local interactions. We consider explicitly both the morphologically stable case, and…

Statistical Mechanics · Physics 2014-01-28 Matteo Nicoli , Rodolfo Cuerno , Mario Castro

The statistics of the fluctuations of quantum many-body systems are highly revealing of their nature. In driven-dissipative systems displaying macroscopic quantum coherence, as exciton polariton condensates under incoherent pumping, the…

We extend the previously developed weak noise scheme, applied to the noisy Burgers equation in 1D, to the Kardar-Parisi-Zhang equation for a growing interface in arbitrary dimensions. By means of the Cole-Hopf transformation we show that…

Statistical Mechanics · Physics 2007-05-23 Hans C. Fogedby

We study fluctuations of interfaces in the Kardar-Parisi-Zhang (KPZ) universality class with curved initial conditions. By simulations of a cluster growth model and experiments of liquid-crystal turbulence, we determine the universal…

Statistical Mechanics · Physics 2020-02-13 Yohsuke T. Fukai , Kazumasa A. Takeuchi

We study the interface dynamics of a discrete model to quantitatively describe electrochemical deposition experiments. Extensive numerical simulations indicate that the interface dynamics is unstable at early times, but asymptotically…

Statistical Mechanics · Physics 2016-08-15 Mario Castro , Rodolfo Cuerno , Angel S\anchez , Francisco Domínguez-Adame

The Kardar-Parisi-Zhang (KPZ) equation is a celebrated non-linear stochastic equation featuring non-equilibrium scaling. Although in one dimension, its statistical properties are very well understood, a new scaling regime has been reported…

Statistical Mechanics · Physics 2025-12-04 Liubov Gosteva , Nicolás Wschebor , Léonie Canet

We study the competitive RSOS-BD model focusing on the validity of the Kardar-Parisi-Zhang (KPZ) ansatz h(t) = v t + (\Gamma t)^{\beta} \chi and the universality of the height distributions (HDs) near the point where the model has…

Statistical Mechanics · Physics 2013-03-14 Tiago J. Oliveira