相关论文: Constructing a solution of the $(2+1)$-dimensional…
We study numerically the Kuramoto-Sivashinsky (KS) equation forced by external white noise in two space dimensions, that is a generic model for e.g. surface kinetic roughening in the presence of morphological instabilities. Large scale…
We propose a mean field theory for interfaces growing according to the Kardar-Parisi-Zhang (KPZ) equation in 1+1 dimensions. The mean field equations are formulated in terms of densities at different heights, taking surface tension and the…
The Kardar-Parisi-Zhang (KPZ) equation is a celebrated non-linear stochastic dynamical equation yielding non-equilibrium universal scaling. It exhibits notorious non-perturbative aspects. The KPZ fixed point is strong-coupling, all the more…
We consider the $(1+1)$-dimensional stochastic heat equation (SHE) with multiplicative white noise and the Cole-Hopf solution of the Kardar-Parisi-Zhang (KPZ) equation. We show an exact way of computing the Lyapunov exponents of the SHE for…
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…
We present numerical Monte Carlo results for the stationary state properties of KPZ type growth in two dimensional surfaces, by evaluating the finite size scaling (FSS) behaviour of the 2nd and 4th moments, $W_2$ and $W_4$, and the…
We study the directed polymer (DP) of length $t$ in a random potential in dimension 1+1 in the continuum limit, with one end fixed and one end free. This maps onto the Kardar-Parisi-Zhang growth equation in time $t$, with flat initial…
We study discrete KPZ growth models deposited on square lattice substrates, whose (average) lateral size enlarges as $L= L_0 + \omega t^{\gamma}$. Our numerical simulations reveal that the competition between the substrate expansion and the…
A modified Kardar-Parisi-Zhang (KPZ) equation is introduced, and solved exactly in the infinite-range limit. In the low-noise limit the system exhibits a weak-to-strong coupling transition, rounded for non-zero noise, as a function of the…
We consider a natural class of $\mathbf{R}^d$-valued one-dimensional stochastic PDEs driven by space-time white noise that is formally invariant under the action of the diffeomorphism group on $\mathbf{R}^d$. This class contains in…
Our understanding of the one-dimensional KPZ equation, \textit{alias} noisy Burgers equation, has advanced substantially over the past five years. We provide a non-technical review, where we limit ourselves to the stochastic PDE and lattice…
We introduce the notion of energy solutions of the KPZ equation. Under minimal assumptions, we prove that the density fluctuations of one-dimensional, weakly asymmetric, conservative particle systems with respect to the stationary states…
We study parametric amplification of Kaluza-Klein (KK) modes in a higher $D$-dimensional generalized Kaluza-Klein theory, which was originally considered by Mukohyama in the narrow resonance case. It was suggested that KK modes can be…
It is shown that the mode-coupling equations for the strong-coupling limit of the KPZ equation have a solution for d>4 such that the dynamic exponent z is 2 (with possible logarithmic corrections) and that there is a delta function term in…
We derive the KPZ equation as a continuum limit of height functions in asymmetric simple exclusion processes with drift that depends on the local particle configuration. To our knowledge, it is a first such result for a class of particle…
We introduce a framework, which is a mesoscopic-fluctuation-scale analog of Yau's method [46] for hydrodynamic limits, for deriving KPZ equations with time-dependent coefficients from time-inhomogeneous interacting particle systems. To our…
We investigate the behavior of the zero-temperature quantum non-linear sigma model in d dimensions in the presence of a damping term of the form f(w)~ |w|^alpha, with 1 \le alpha <2. We find two fixed points: a spin-wave fixed point FP1…
The short-time evolution of a growing interface is studied analytically and numerically for the Kadar-Parisi-Zhang (KPZ) universality class. The scaling behavior of response and correlation functions is reminiscent of the ``initial slip''…
The formation of singularities in solutions to the dispersionless Kadomtsev-Petviashvili (dKP) equation is studied numerically for different classes of initial data. The asymptotic behavior of the Fourier coefficients is used to…
The classical Heisenberg model has been solved in spatial d dimensins, exactly in d=1 and by the Migdal-Kadanoff approximation in d>1, by using a Fourier-Legendre expansion. The phase transition temperatures, the energy densities, and the…