Related papers: Local KPZ behavior under arbitrary scaling limits
We study the surface dynamics of silica films grown by low pressure chemical vapor deposition. Atomic force microscopy measurements show that the surface reaches a scale invariant stationary state compatible with the Kardar-Parisi-Zhang…
We simulate a growth model with restricted surface relaxation process in d=1 and d=2, where d is the dimensionality of a flat substrate. In this model, each particle can relax on the surface to a local minimum, as the Edwards-Wilkinson…
We investigate the Kardar--Parisi--Zhang (KPZ) equation in $d$ spatial dimensions with Gaussian spatially long--range correlated noise --- characterized by its second moment $R(\vec{x}-\vec{x}') \propto |\vec{x}-\vec{x}'|^{2\rho-d}$ --- by…
Kardar-Parisi-Zhang (KPZ) equation is a quasilinear stochastic partial differential equation(SPDE) driven by a space-time white noise. In recent years there have been several works directed towards giving a rigorous meaning to a solution of…
A host of spatially extended systems, both in physics and in other disciplines, are well described at a coarse-grained scale by a Langevin equation with multiplicative-noise. Such systems may exhibit non-equilibrium phase transitions, which…
Stochastic motion of a point -- known as Brownian motion -- has many successful applications in science, thanks to its scale invariance and consequent universal features such as Gaussian fluctuations. In contrast, the stochastic motion of a…
Universal behavior in far-from-equilibrium systems is driven by interactions between transport processes and noise structure. The Kardar-Parisi-Zhang (KPZ) framework predicts that extensions incorporating conserved currents or temporally…
We explore linear control of the one-dimensional non-linear Kardar--Parisi--Zhang (KPZ) equation with the goal to understand the effects the control process has on the dynamics and on the stationary state of the resulting stochastic growth…
We investigate the infinite-dimensional limit of nonequilibrium surface growth by numerically integrating stochastic growth equations on a fully connected graph. In particular, we study the Edwards-Wilkinson (EW), Kardar-Parisi-Zhang (KPZ),…
We study ageing during surface growth processes described by the one-dimensional Kardar-Parisi-Zhang equation. Starting from a flat initial state, the systems undergo simple ageing in both correlators and linear responses and its dynamical…
We consider the KPZ equation in space dimension 2 driven by space-time white noise. We showed in previous work that if the noise is mollified in space on scale $\epsilon$ and its strength is scaled as $\hat\beta / \sqrt{|\log \epsilon|}$,…
Numerical analysis of conserved field dynamics has been generally performed with pseudo spectral methods. Finite differences integration, the common procedure for non-conserved field dynamics, indeed struggles to implement a conservative…
We introduce a self-organized surface growth model in 2+1 dimensions with anisotropic avalanche process, which is expected to be in the universality class of the anisotropic quenched Kardar-Parisi-Zhang equation with alternative signs of…
We investigate the universal behavior of the Kardar-Parisi-Zhang (KPZ) equation with temporally correlated noise. The presence of time correlations in the microscopic noise breaks the statistical tilt symmetry, or Galilean invariance, of…
The $(d+1)$-dimensional KPZ equation is the canonical model for the growth of rough $d$-dimensional random surfaces. A deep mathematical understanding of the KPZ equation for $d=1$ has been achieved in recent years, and the case $d\ge 3$…
We present an analytical method, rooted in the non-perturbative renormalization group, that allows one to calculate the critical exponents and the correlation and response functions of the Kardar-Parisi-Zhang (KPZ) growth equation in all…
Growth of interfaces during vapor deposition are analyzed on a discrete lattice. Foe a rough surface, relation between the roughness exponent alpha, and corresponding step-step (slope-slope) couplings is obtained in (1+1) and (2+1)…
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…
Characterizing how entanglement grows with time in a many-body system, for example after a quantum quench, is a key problem in non-equilibrium quantum physics. We study this problem for the case of random unitary dynamics, representing…
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…