Competing Universalities in Kardar-Parisi-Zhang (KPZ) Growth Models

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 probability for the initially flat geometry to be chosen and compute the phase diagram as a function of p. We find that the distribution of the fluctuations converges to the Gaussian orthogonal ensemble Tracy-Widom (TW) distribution for p0.5. For p=0.5 where the two geometries are equally weighted, the behavior is governed by an emergent Gaussian statistics in the universality class of Brownian motion. We propose a phenomenological theory to explain our findings and discuss possible applications in nonequilibrium transport and traffic flow.Comment: 5 pages, 6 figures, Phys. Rev. Lett. (2019) (accepted

An exactly solvable record model for rainfall

Daily precipitation time series are composed of null entries corresponding to dry days and nonzero entries that describe the rainfall amounts on wet days. Assuming that wet days follow a Bernoulli process with success probability $p$, we show that the presence of dry days induces negative correlations between record-breaking precipitation events. The resulting non-monotonic behavior of the Fano factor of the record counting process is recovered in empirical data. We derive the full probability distribution $P(R,n)$ of the number of records $R_n$ up to time $n$, and show that for large $n$, its large deviation form coincides with that of a Poisson distribution with parameter $\ln(p\,n)$. We also study in detail the joint limit $p \to 0$, $n \to \infty$, which yields a random record model in continuous time $t = pn$.Comment: 11 pages, 2 figures + 13 pages and 2 figures of supplemental materia

New mechanism for impurity-induced step bunching

Codeposition of impurities during the growth of a vicinal surface leads to an impurity concentration gradient on the terraces, which induces corresponding gradients in the mobility and the chemical potential of the adatoms. Here it is shown that the two types of gradients have opposing effects on the stability of the surface: Step bunching can be caused by impurities which either lower the adatom mobility, or increase the adatom chemical potential. In particular, impurities acting as random barriers (without affecting the adatom binding) cause step bunching, while for impurities acting as random traps the combination of the two effects reduces to a modification of the attachment boundary conditions at the steps. In this case attachment to descending steps, and thus step bunching, is favored if the impurities bind adatoms more weakly than the substrate.Comment: 7 pages, 3 figures. Substantial revisions and correction

Kinetic Roughening in Deposition with Suppressed Screening

Models of irreversible surface deposition of k-mers on a linear lattice, with screening suppressed by disallowing overhangs blocking large gaps, are studied by extensive Monte Carlo simulations of the temporal and size dependence of the growing interface width. Despite earlier finding that for such models the deposit density tends to increase away from the substrate, our numerical results place them clearly within the standard KPZ universality class.Comment: nine pages, plain TeX (4 figures not included

Symmetry analysis of magneto-optical effects: The case of x-ray diffraction and x-ray absorption at the transition metal L23 edge

A general symmetry analysis of the optical conductivity or scattering tensor is used to rewrite the conductivity tensor as a sum of fundamental spectra multiplied by simple functions depending on the local magnetization direction. Using this formalism, we present several numerical examples at the transition metal L23 edge. From these numerical calculations we can conclude that large deviations from the magneto-optical effects in spherical symmetry are found. These findings are in particular important for resonant x-ray diffraction experiments where the polarization dependence and azimuthal dependence of the scattered Bragg intensity is used to determine the local ordered magnetization direction

Persistence exponents for fluctuating interfaces

Numerical and analytic results for the exponent \theta describing the decay of the first return probability of an interface to its initial height are obtained for a large class of linear Langevin equations. The models are parametrized by the dynamic roughness exponent \beta, with 0 < \beta < 1; for \beta = 1/2 the time evolution is Markovian. Using simulations of solid-on-solid models, of the discretized continuum equations as well as of the associated zero-dimensional stationary Gaussian process, we address two problems: The return of an initially flat interface, and the return to an initial state with fully developed steady state roughness. The two problems are shown to be governed by different exponents. For the steady state case we point out the equivalence to fractional Brownian motion, which has a return exponent \theta_S = 1 - \beta. The exponent \theta_0 for the flat initial condition appears to be nontrivial. We prove that \theta_0 \to \infty for \beta \to 0, \theta_0 \geq \theta_S for \beta 1/2, and calculate \theta_{0,S} perturbatively to first order in an expansion around the Markovian case \beta = 1/2. Using the exact result \theta_S = 1 - \beta, accurate upper and lower bounds on \theta_0 can be derived which show, in particular, that \theta_0 \geq (1 - \beta)^2/\beta for small \beta.Comment: 12 pages, REVTEX, 6 Postscript figures, needs multicol.sty and epsf.st

Morphological stability of electromigration-driven vacancy islands

The electromigration-induced shape evolution of two-dimensional vacancy islands on a crystal surface is studied using a continuum approach. We consider the regime where mass transport is restricted to terrace diffusion in the interior of the island. In the limit of fast attachment/detachment kinetics a circle translating at constant velocity is a stationary solution of the problem. In contrast to earlier work [O. Pierre-Louis and T.L. Einstein, Phys. Rev. B 62, 13697 (2000)] we show that the circular solution remains linearly stable for arbitrarily large driving forces. The numerical solution of the full nonlinear problem nevertheless reveals a fingering instability at the trailing end of the island, which develops from finite amplitude perturbations and eventually leads to pinch-off. Relaxing the condition of instantaneous attachment/detachment kinetics, we obtain non-circular elongated stationary shapes in an analytic approximation which compares favorably to the full numerical solution.Comment: 12 page

Driven Lattice Gases with Quenched Disorder: Exact Results and Different Macroscopic Regimes

We study the effect of quenched spatial disorder on the steady states of driven systems of interacting particles. Two sorts of models are studied: disordered drop-push processes and their generalizations, and the disordered asymmetric simple exclusion process. We write down the exact steady-state measure, and consequently a number of physical quantities explicitly, for the drop-push dynamics in any dimensions for arbitrary disorder. We find that three qualitatively different regimes of behaviour are possible in 1-$d$ disordered driven systems. In the Vanishing-Current regime, the steady-state current approaches zero in the thermodynamic limit. A system with a non-zero current can either be in the Homogeneous regime, chracterized by a single macroscopic density, or the Segregated-Density regime, with macroscopic regions of different densities. We comment on certain important constraints to be taken care of in any field theory of disordered systems.Comment: RevTex, 17pages, 18 figures included using psfig.st

Kinetic roughening of surfaces: Derivation, solution and application of linear growth equations

We present a comprehensive analysis of a linear growth model, which combines the characteristic features of the Edwards--Wilkinson and noisy Mullins equations. This model can be derived from microscopics and it describes the relaxation and growth of surfaces under conditions where the nonlinearities can be neglected. We calculate in detail the surface width and various correlation functions characterizing the model. In particular, we study the crossover scaling of these functions between the two limits described by the combined equation. Also, we study the effect of colored and conserved noise on the growth exponents, and the effect of different initial conditions. The contribution of a rough substrate to the surface width is shown to decay universally as $w_i(0) (\xi_s/\xi(t))^{d/2}$, where $\xi(t) \sim t^{1/z}$ is the time--dependent correlation length associated with the growth process, $w_i(0)$ is the initial roughness and $\xi_s$ the correlation length of the substrate roughness, and $d$ is the surface dimensionality. As a second application, we compute the large distance asymptotics of the height correlation function and show that it differs qualitatively from the functional forms commonly used in the intepretation of scattering experiments.Comment: 28 pages with 4 PostScript figures, uses titlepage.sty; to appear in Phys. Rev.