Related papers: The Kardar-Parisi-Zhang equation - a statistical p…
In the first part of this work the classical and statistical aspects of the dynamics of an inextensible chain in three dimensions are investigated. In the second part the special case of a chain admitting only fixed angles with respect to…
We identify the key features of Kardar-Parisi-Zhang universality class in the fluctuations of the wave density logarithm, in a two-dimensional Anderson localized wave packet. In our numerical analysis, the fluctuations are found to exhibit…
We consider the scaling limits for a one-dimensional random growth model, the weakly asymmetric single step Solid-on-Solid process. We show that the fluctuation field, if considered in an appropriate (long) space-time scale, solves the…
Dynamical universality classes are distinguished by their dynamical exponent $z$ and unique scaling functions encoding space-time asymmetry for, e.g. slow-relaxation modes or the distribution of time-integrated currents. So far the…
We study the scaling regimes for the Kardar-Parisi-Zhang equation with noise correlator R(q) ~ (1 + w q^{-2 \rho}) in Fourier space, as a function of \rho and the spatial dimension d. By means of a stochastic Cole-Hopf transformation, the…
The Kardar-Parisi-Zhang model of non-equilibrium critical behaviour (kinetic surface roughening) with turbulent motion of the environment taken into account is studied by the field theoretic renormalization group approach. The turbulent…
We study a generalized Kardar-Parisi-Zhang (KPZ) equation [Jana et al., Phys. Rev. E 109, L032104 (2024)] that sets the paradigm for universality in roughening of growing nonequilibrium surfaces without any conservation laws but with…
We simulate the Kardar-Parisi-Zhang equation in 2+1 dimensions. The Hopf-Cole transformation is used in order to obtain a stable numerical scheme. The two relevant critical exponents are precisely measured. (2 PostScript figures available…
While stretching of a polymer along a flat surface is hardly different from the classical Pincus problem of pulling chain ends in free space, the role of curved geometry in conformational statistics of the stretched chain is an exciting…
We discuss the features of nonequilibrium growth problems, their scaling description and their differences from equilibrium problems. The emphasis is on the Kardar-Parisi-Zhang equation and the renormalization group point of view. Some of…
We report on the universality of height fluctuations at the crossing point of two interacting (1+1)-dimensional Kardar-Parisi-Zhang (KPZ) interfaces with curved and flat initial conditions. We introduce a control parameter p as the…
The one dimensional Kardar-Parisi-Zhang universality class is believed to describe many types of evolving interfaces which have the same characteristic scaling exponents. These exponents lead to a natural renormalization/rescaling on the…
We show that the distribution of the time delay for one-dimensional random potentials is universal in the high energy or weak disorder limit. Our analytical results are in excellent agreement with extensive numerical simulations carried out…
We study the phase turbulence of the one-dimensional complex Ginzburg-Landau equation, in which the defect-free chaotic dynamics of the order parameter maps to a phase equation well approximated by the Kuramoto-Sivashinsky model. In this…
The determination of the exact exponents of the KPZ class in any substrate dimension $d$ is one of the most important open issues in Statistical Physics. Based on the behavior of the dimensional variation of some exact exponent differences…
The controversy whether or not he Kardar-Parisi-Zhang (KPZ) equation has an upper critical dimension (UCD) is going on for quite a long time. Some approximate integral equations for the two-point function served as an indication for the…
A growing interface subject to noise is described by the Kardar-Parisi-Zhang equation or, equivalently, the noisy Burgers equation. In one dimension this equation is analyzed by means of a weak noise canonical phase space approach applied…
Integrable probability has emerged as an active area of research at the interface of probability/mathematical physics/statistical mechanics on the one hand, and representation theory/integrable systems on the other. Informally, integrable…
This paper concerns the multi-component coupled Kardar-Parisi-Zhang (KPZ) equation and its two types of approximations. One approximation is obtained as a simple replacement of the noise term by a smeared noise with a proper…
This paper concerns the existence of global weak solutions \`a la Leray for compressible Navier-Stokes equations with a pressure law that depends on the density and on time and space variables $t$ and $x$. The assumptions on the pressure…