Related papers: Glassy Solutions of the Kardar-Pasrisi-Zhang Equat…
We re-examine mode-coupling theory for the Kardar-Parisi-Zhang (KPZ) equation in the strong coupling limit and show that there exists two branches of solutions. One branch (or universality class) only exists for dimensionalities $d<d_c=2$…
We study the mode-coupling approximation for the KPZ equation in the strong coupling regime. By constructing an ansatz consistent with the asymptotic forms of the correlation and response functions we determine the upper critical dimension…
The strong-coupling regime of Kardar-Parisi-Zhang surface growth driven by short-ranged noise has an upper critical dimension d_> less or equal to four (where the dynamic exponent z takes the value z (d_>) = 2). To derive this, we use the…
We study in this series of articles the Kardar-Parisi-Zhang (KPZ) equation $$ \partial_t h(t,x)=\nu\Delta h(t,x)+\lambda V(|\nabla h(t,x)|) +\sqrt{D}\, \eta(t,x), \qquad x\in{\mathbb{R}}^d $$ in $d\ge 1$ dimensions. The forcing term $\eta$…
We have studied the Kardar-Parisi-Zhang equation in the strong coupling regime in the mode-coupling approximation. We solved numerically in dimension d=1 for the correlation function at wavevector k. At large times t we found the predicted…
We present an exact solution of the {\it deterministic} Kardar-Parisi-Zhang (KPZ) equation under the influence of a local driving force $f$. For substrate dimension $d \le 2$ we recover the well-known result that for arbitrarily small…
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…
A master equation for the Kardar-Parisi-Zhang (KPZ) equation in 2+1 dimensions is developed. In the fully nonlinear regime we derive the finite time scale of the singularity formation in terms of the characteristics of forcing. The exact…
We revisit the Lieb-Liniger model for $n$ bosons in one dimension with attractive delta interaction in a half-space $\mathbb{R}^+$ with diagonal boundary conditions. This model is integrable for arbitrary value of $b \in \mathbb{R}$, the…
We study in the present article the Kardar-Parisi-Zhang (KPZ) equation $$ \partial_t h(t,x)=\nu\Delta h(t,x)+\lambda |\nabla h(t,x)|^2 +\sqrt{D}\, \eta(t,x), \qquad (t,x)\in\mathbb{R}_+\times\mathbb{R}^d $$ in $d\ge 3$ dimensions in the…
The Kardar-Parisi-Zhang universality class of stochastic surface growth is studied by exact field-theoretic methods. From previous numerical results, a few qualitative assumptions are inferred. In particular, height correlations should…
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 construct the equations for the growth kinetics of an aging structural glass within mode-coupling theory through a non-stationary variant of the 3-density correlator defined in Phys. Rev. Lett. {\bf 97}, 195701 (2006). We solve a…
The celebrated Kardar-Parisi-Zhang (KPZ) equation describes the kinetic roughening of stochastically growing interfaces. In one dimension, the KPZ equation is exactly solvable and its statistical properties are known to an exquisite degree.…
We study the atypically large deviations of the height $H \sim {{\cal O}}(t)$ at the origin at late times in $1+1$-dimensional growth models belonging to the Kardar-Parisi-Zhang (KPZ) universality class. We present exact results for the…
Large scale, dynamical simulations have been performed for the two dimensional octahedron model, describing the Kardar-Parisi-Zhang (KPZ) for nonlinear, or the Edwards-Wilkinson (EW) class for linear surface growth. The autocorrelation…
We study the solution of the Kardar-Parisi-Zhang (KPZ) equation for the stochastic growth of an interface of height $h(x,t)$ on the positive half line, equivalently the free energy of the continuum directed polymer in a half space with a…
The Kardar-Parisi-Zhang (KPZ) equation of nonlinear stochastic growth in d dimensions is studied using the mapping onto a system of directed polymers in a quenched random medium. The polymer problem is renormalized exactly in a minimally…
The one-dimensional Kardar-Parisi-Zhang dynamic interface growth equation with the self-similar Ansatz is analyzed. As a new feature additional analytic terms are added. From the mathematical point of view, these can be considered as…
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…