相关论文: On Time Correlations for KPZ Growth in One Dimensi…
We obtain a simple formula for the stationary measure of the height field evolving according to the Kardar-Parisi-Zhang equation on the interval $[0,L]$ with general Neumann type boundary conditions and any interval size. This is achieved…
We investigate solid-on-solid models that belong to the Kardar-Parisi-Zhang (KPZ) universality class on substrates that expand laterally at a constant rate by duplication of columns. Despite the null global curvature, we show that all…
In discrete models describing growing rough interfaces of the Kardar-Parisi-Zhang universality class, we examine height fluctuations at a fixed site as a function of time in the monolayer unit. For small systems, we show that it is possible…
Obtaining the exact multi-time correlations for one-dimensional growth models described by the Kardar-Parisi-Zhang (KPZ) universality class is presently an outstanding open problem. Here, we study the joint probability distribution function…
We study the dynamics of a growing crystalline facet where the growth mechanism is controlled by the geometry of the local curvature. A continuum model, in (2+1) dimensions, is developed in analogy with the Kardar-Parisi-Zhang (KPZ) model…
Stochastic partial differential equations can be used to model second order thermodynamical phase transitions, as well as a number of critical out-of-equilibrium phenomena. In (2+1) dimensions, many of these systems are conjectured (and…
The Kardar-Parisi-Zhang (KPZ) equation for surface growth has been analyzed for over three decades. Some experiments indicated the power law for the interface width, $w(t)\sim t^\beta$, remains the same as in growth on planar surfaces.…
The phenomenon of stochastic growth of a surface on a two-dimensional substrate occurs in Nature in a variety of circumstances and its statistical characterization requires the study of higher order cumulants. Here, we consider the…
The deposition dynamics of particles (or the growth of a rigid crystal) on a disordered substrate at a finite deposition rate is explored. We begin with an equation of motion which includes, in addition to the disorder, the periodic…
We study the synchronization physics of 1D and 2D oscillator lattices subject to noise and predict a dynamical transition that leads to a sudden drastic increase of phase diffusion. Our analysis is based on the widely applicable…
The time-dependent probability distribution function of the height for the Kardar-Parisi-Zhang equation with sharp wedge initial conditions has been obtained recently as a convolution between the Gumbel distribution and a difference of two…
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…
Circular KPZ interfaces spreading radially in the plane have GUE Tracy-Widom (TW) height distribution (HD) and Airy$_2$ spatial covariance, but what are their statistics if they evolve on the surface of a different background space, such as…
We construct a family of stochastic growth models in 2+1 dimensions, that belong to the anisotropic KPZ class. Appropriate projections of these models yield 1+1 dimensional growth models in the KPZ class and random tiling models. We show…
Consider a deterministically growing surface of any dimension, where the growth at a point is an arbitrary nonlinear function of the heights at that point and its neighboring points. Assuming that this nonlinear function is monotone,…
We obtain several exact results for universal distributions involving the maximum of the Airy$_2$ process minus a parabola and plus a Brownian motion, with applications to the 1D Kardar-Parisi-Zhang (KPZ) stochastic growth universality…
After a brief introduction we review the nonperturbative weak noise approach to the KPZ equation in one dimension. We argue that the strong coupling aspects of the KPZ equation are related to the existence of localized propagating domain…
We consider the Kardar-Parisi-Zhang equation on the interval $[0,L]$ with Neumann type boundary conditions and boundary parameters $u,v$. We show that the $k$-th order cumulant of the height behaves as $c_k(L,u,v)\, t$ in the large time…
We consider the lattice dynamics in the half-space. The initial data are random according to a probability measure which enforces slow spatial variation on the linear scale $\varepsilon^{-1}$. We establish two time regimes. For times of…
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).…