Related papers: Kardar-Parisi-Zhang Equation from Long-Range Exclu…
We study the short-time behavior of the probability distribution $\mathcal{P}(H,t)$ of the surface height $h(x=0,t)=H$ in the Kardar-Parisi-Zhang (KPZ) equation in $1+1$ dimension. The process starts from a stationary interface: $h(x,t=0)$…
We discuss the universal behavior linked to the Goldstone mode associated with the spontaneous breaking of time-translation symmetry in many-body systems, in which the order parameter traces out a limit cycle. We show that this universal…
We present a systematic discretization scheme for the Kardar-Parisi-Zhang (KPZ) equation, which correctly captures the strong-coupling properties of the continuum model. In particular we show that the scheme contains no finite-time…
We apply a number of schemes which variationally improve perturbation theory for the Kardar-Parisi-Zhang equation in order to extract estimates for the dynamic exponent z. The results for the various schemes show the same broad features,…
The probabilities $P_\pm(t_0,t)$ that a growing Kardar-Parisi-Zhang interface remains above or below the mean height in the time interval $(t_0, t)$ are shown numerically to decay as $P_\pm \sim (t_0/t)^{\theta_\pm}$ with $\theta_+ = 1.18…
We study the ballistic deposition and the grain deposition models on two-dimensional substrates. Using the Kardar-Parisi-Zhang (KPZ) ansatz for height fluctuations, we show that the main contribution to the intrinsic width, which causes…
Many models of one-dimensional local random growth are expected to lie in the Kardar-Parisi-Zhang (KPZ) universality class. For such a model, the interface profile at advanced time may be viewed in scaled coordinates specified via…
We have simulated an automaton version of the quenched Kardar-Parisi-Zhang (qKPZ) equation in one and two dimensions in order to study the scaling properties of the interface at the depinning transition. Specifically, the $\alpha$, $\beta$,…
This paper studies the large scale limits of multi-type invariant distributions and Busemann functions of planar stochastic growth models in the Kardar-Parisi-Zhang (KPZ) class. We identify a set of sufficient hypotheses for convergence of…
For stationary interface growth, governed by the Kardar-Parisi-Zhang (KPZ) equation in 1 + 1 dimensions, typical fluctuations of the interface height at long times are described by the Baik-Rains distribution. Recently Chhita et al. [1]…
Integrable spin chains with a continuous non-Abelian symmetry, such as the one-dimensional isotropic Heisenberg model, show superdiffusive transport with little theoretical understanding. Although recent studies reported a surprising…
The Kardar-Parisi-Zhang (KPZ) universality class describes a large class of 2-dimensional models of random growth, which exhibit universal scaling exponents and limiting statistics. The last ten years has seen remarkable progress in this…
We consider some models in the Kardar-Parisi-Zhang universality class, namely the polynuclear growth model and the totally/partially asymmetric simple exclusion process. For these models, in the limit of large time t, universality of…
We consider the asymmetric simple exclusion process (ASEP) on the positive integers with an open boundary condition. We show that, when starting devoid of particles and for a certain boundary condition, the height function at the origin…
The roughening of interfaces moving in inhomogeneous media is investigated by numerical integration of the phenomenological stochastic differential equation proposed by Kardar, Parisi, and Zhang [Phys. Rev. Lett. 56, 889, (1986)] with…
We study the mode-coupling theory for the Kardar-Parisi-Zhang equation in the strong-coupling regime, focusing on the long time properties. By a saddle point analysis of the mode-coupling equations, we derive exact results for the…
We introduce a non-perturbative renormalization approach which identifies stable fixed points in any dimension for the Kardar-Parisi-Zhang dynamics of rough surfaces. The usual limitations of real space methods to deal with anisotropic…
We investigate the stationary-state fluctuations of a growing one-dimensional interface described by the KPZ dynamics with a noise featuring smooth spatial correlations of characteristic range $\xi$. We employ Non-perturbative Functional…
There have been recently several works studying the regularized stochastic heat equation (SHE) and Kardar-Parisi-Zhang (KPZ) equation in dimension $d\geq 3$ as the smoothing parameter is switched off, but most of the results did not hold in…
Equilibrium and nonequilibrium states of matter can exhibit fundamentally different behavior. A key example is the Kardar-Parisi-Zhang universality class in two spatial dimensions (2D KPZ), where microscopic deviations from equilibrium give…