Related papers: Some recent progress on the periodic KPZ equation
The nonequilibrium steady state of the one-dimensional (1D) Kardar-Parisi-Zhang (KPZ) universality class is studied in-depth by exact solutions, yet no direct experimental evidence of its characteristic statistical properties has been…
We study exact stationary properties of the one-dimensional Kardar-Parisi-Zhang (KPZ) equation by using the replica approach. The stationary state for the KPZ equation is realized by setting the initial condition the two-sided Brownian…
In this work, the out-of-equilibrium dynamics of the Kardar-Parisi-Zhang equation in (1+1) dimensions is studied by means of numerical simulations, focussing on the two-times evolution of an interface in the absence of any disordered…
We propose a unified moving boundary problem for surface growth by electrochemical and chemical vapor deposition, which is derived from constitutive equations into which stochastic forces are incorporated. We compute the coefficients in the…
We study the probability distribution $\mathcal{P}(H,t,L)$ of the surface height $h(x=0,t)=H$ in the Kardar-Parisi-Zhang (KPZ) equation in $1+1$ dimension when starting from a parabolic interface, $h(x,t=0)=x^2/L$. The limits of…
We integrate numerically the Kardar-Parisi-Zhang (KPZ) equation in 1+1 and 2+1 dimensions using an Euler discretization scheme and the replacement of ${(\nabla h)}^2$ by exponentially decreasing functions of that quantity to suppress…
In this paper, we introduce a novel integration method of Kardar-Parisi-Zhang (KPZ) equation. It has always been known that if during the discrete integration of the KPZ equation the nearest-neighbor height-difference exceeds a critical…
A model for kinetic roughening of one-dimensional interfaces is presented within an intrinsic geometry framework that is free from the standard small-slope and no-overhang approximations. The model is meant to probe the consequences of the…
We investigate Kardar-Parisi-Zhang (KPZ) surface growth in the presence of long-term correlated noise. By means of extensive numerical simulations of models in the KPZ universality class we find that, as the noise correlator range…
The short-time evolution of a growing interface is studied within the framework of the dynamic renormalization group approach for the Kadar-Parisi-Zhang (KPZ) equation and for an idealized continuum model of molecular beam epitaxy (MBE).…
Growth of interfaces during vapor deposition is analyzed on a discrete lattice. It leads to finding distribution of local heights, measurable for any lattice model. Invariance in the change of this distribution in time is used to determine…
We give a brief overview of the seminal paper which introduced the Kardar-Parisi-Zhang equation as a paradigmatic model for random growth in 1986. We describe some of the developments to which it gave rise in mathematics and physics over…
In this work we write down a classical (not quantum) action for the surface height for the Kardar-Parisi-Zhang (KPZ) equation for surface growth. We do so starting with the regular Martin-Siggia-Rose (MSR) action (which is quantum -…
We consider the Cole-Hopf solution of the (1+1)-dimensional KPZ equation started from the narrow wedge initial condition. In this article, we ask how the peaks and valleys of the KPZ height function (centered by time/24) at any spatial…
The Kardar-Parisi-Zhang (KPZ) equation is conjectured to universally describe the fluctuations of weakly asymmetric interface growth. Here we provide the first intrinsic well-posedness result for the KPZ equation on the real line by showing…
The Kardar-Parisi-Zhang (KPZ) fixed point is a Markov process that is conjectured to be at the core of the KPZ universality class. In this article we study two aspects the KPZ fixed point that share the same Brownian limiting behaviour: the…
This Letter reports on how the interfaces in the (1+1)-dimensional Kardar-Parisi-Zhang (KPZ) class undergo, in the course of time, a transition from the flat, growing regime to the stationary one. Simulations of the polynuclear growth model…
The stochastic PDE known as the Kardar-Parisi-Zhang equation (KPZ) has been proposed as a model for a randomly growing interface. This equation can be reformulated as a stochastic Burgers equation. We study a stochastic KdV-Burgers equation…
The Kardar-Parisi-Zhang (KPZ) universality class describes a broad range of non-equilibrium fluctuations, including those of growing interfaces, directed polymers and particle transport, to name but a few. Since the year 2000, our…
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…