Comment on "Dynamic Scaling of Non-Euclidean Interfaces" [arXiv:0804.1898]

This is the revised version of a Comment on a paper by C. Escudero (Phys. Rev. Lett. 100, 116101, 2008; arXiv:0804.1898)

Anti-Coarsening and Complex Dynamics of Step Bunches on Vicinal Surfaces during Sublimation

A sublimating vicinal crystal surface can undergo a step bunching instability when the attachment-detachment kinetics is asymmetric, in the sense of a normal Ehrlich-Schwoebel effect. Here we investigate this instability in a model that takes into account the subtle interplay between sublimation and step-step interactions, which breaks the volume-conserving character of the dynamics assumed in previous work. On the basis of a systematically derived continuum equation for the surface profile, we argue that the non-conservative terms pose a limitation on the size of emerging step bunches. This conclusion is supported by extensive simulations of the discrete step dynamics, which show breakup of large bunches into smaller ones as well as arrested coarsening and periodic oscillations between states with different numbers of bunches.Comment: 26 pages, 11 figure

Power laws in surface physics: The deep, the shallow and the useful

The growth and dynamics of solid surfaces displays a multitude of power law relationships, which are often associated with geometric self-similarity. In many cases the mechanisms behind these power laws are comparatively trivial, and require little more than dimensional analysis for their derivation. The information of interest to surface physicists then resides in the prefactors. This point will be illustrated by recent experimental and theoretical work on the growth-induced roughening of thin films and step fluctuations on vicinal surfaces. The conventional distinction between trivial and nontrivial power laws will be critically examined in general, and specifically in the context of persistence of step fluctuations.Comment: To appear in a special issue of Physica A in memory of Per Ba

Dynamic phase transitions in electromigration-induced step bunching

Electromigration-induced step bunching in the presence of sublimation or deposition is studied theoretically in the attachment-limited regime. We predict a phase transition as a function of the relative strength of kinetic asymmetry and step drift. For weak asymmetry the number of steps between bunches grows logarithmically with bunch size, whereas for strong asymmetry at most a single step crosses between two bunches. In the latter phase the emission and absorption of steps is a collective process which sets in only above a critical bunch size and/or step interaction strength.Comment: 4 pages, 4 figure

Persistence of Kardar-Parisi-Zhang Interfaces

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 $\theta_+ = 1.18 \pm 0.08$ and $\theta_- = 1.64 \pm 0.08$. Bounds on $\theta_\pm$ are derived from the height autocorrelation function under the assumption of Gaussian statistics. The autocorrelation exponent $\bar \lambda$ for a $d$--dimensional interface with roughness and dynamic exponents $\beta$ and $z$ is conjectured to be $\bar \lambda = \beta + d/z$. For a recently proposed discretization of the KPZ equation we find oscillatory persistence probabilities, indicating hidden temporal correlations.Comment: 4 pages, 3 figures, uses revtex and psfi

Kinetics of step bunching during growth: A minimal model

We study a minimal stochastic model of step bunching during growth on a one-dimensional vicinal surface. The formation of bunches is controlled by the preferential attachment of atoms to descending steps (inverse Ehrlich-Schwoebel effect) and the ratio $d$ of the attachment rate to the terrace diffusion coefficient. For generic parameters ($d > 0$) the model exhibits a very slow crossover to a nontrivial asymptotic coarsening exponent $\beta \simeq 0.38$. In the limit of infinitely fast terrace diffusion ($d=0$) linear coarsening ($\beta$ = 1) is observed instead. The different coarsening behaviors are related to the fact that bunches attain a finite speed in the limit of large size when $d=0$, whereas the speed vanishes with increasing size when $d > 0$. For $d=0$ an analytic description of the speed and profile of stationary bunches is developed.Comment: 8 pages, 10 figure

Phase separation in disordered exclusion models

The effect of quenched disorder in the one-dimensional asymmetric exclusion process is reviewed. Both particlewise and sitewise disorder generically induces phase separation in a range of densities. In the particlewise case the existence of stationary product measures in the homogeneous phase implies that the critical density can be computed exactly, while for sitewise disorder only bounds are available. The coarsening of phase-separated domains starting from a homogeneous initial condition is addressed using scaling arguments and extremal statistics considerations. Some of these results have been obtained previously in the context of directed polymers subject to columnar disorder.Comment: 15 pages, 4 figure