Universality issues in surface kinetic roughening of thin solid films

Since publication of the main contributions on the theory of kinetic roughening more than fifteen years ago, many works have been reported on surface growth or erosion that employ the framework of dynamic scaling. This interest was mainly due to the predicted existence of just a few universality classes to describe the statistical properties of the morphology of growing surfaces and interfaces that appear in a wide range of physical systems. Nowadays, this prediction seems to be inaccurate. This situation has caused a clear detriment of these studies in spite of the undeniable existence of kinetic roughening in many different real systems, and without a clear understanding of the reasons behind the mismatch between theoretical expectations and experimental observations. In this chapter we aim to explore existing problems and shortcomings of both the theoretical and experimental approaches, focusing mainly on growth of thin solid films. Our analysis suggests that the theoretical framework as yet is not complete, while more systematic and consistent experiments need to be performed. Once these issues are taken into account, a more consistent and useful theory of kinetic roughening might develop.Comment: Review article to appear in ``Advances in Condensed Matter and Statistical Mechanics", ed. E. Korutcheva and R. Cuerno. To be published by Nova Science Publishers. 22 pages. 4 eps figure

Free Fermionic Elliptic Reflection Matrices and Quantum Group Invariance

Elliptic diagonal solutions for the reflection matrices associated to the elliptic $R$ matrix of the eight vertex free fermion model are presented. They lead through the second derivative of the open chain transfer matrix to an XY hamiltonian in a magnetic field which is invariant under a quantum deformed Clifford--Hopf algebra.Comment: 9 pages, Late

Dynamic effects induced by renormalization in anisotropic pattern forming systems

The dynamics of patterns in large two-dimensional domains remains a challenge in non-equilibrium phenomena. Often it is addressed through mild extensions of one-dimensional equations. We show that full 2D generalizations of the latter can lead to unexpected dynamical behavior. As an example we consider the anisotropic Kuramoto-Sivashinsky equation, that is a generic model of anisotropic pattern forming systems and has been derived in different instances of thin film dynamics. A rotation of a ripple pattern by $90^{\circ}$ occurs in the system evolution when nonlinearities are strongly suppressed along one direction. This effect originates in non-linear parameter renormalization at different rates in the two system dimensions, showing a dynamical interplay between scale invariance and wavelength selection. Potential experimental realizations of this phenomenon are identified.Comment: 5 pages, 3 figures; supplemental material available at journal web page and/or on reques

Quantum symmetries in the free field realization of Wn algebras

7 pages, no figures.-- MSC2000 codes: Primary: 81R50; Secondary: 17B37, 17B81, 81R10.MR#: MR1140143 (92m:81106)$W_n$ algebras are considered in their free field representation to show that they are endowed with a quantum group symmetry which is a $Z_2$ twist à la Drinfel'd of $U_{q+}({\rm sl}(n))\times U_{q-}({\rm sl}(n))$. We use the contour picture of quantum groups due to Gómez and Sierra. A sample computation for the $R$ matrix is also performed.R.C. was supported by a FPI grant by the Spanish MEC.Publicad

Short-range stationary patterns and long-range disorder in an evolution equation for one-dimensional interfaces

A novel local evolution equation for one-dimensional interfaces is derived in the context of erosion by ion beam sputtering. We present numerical simulations of this equation which show interrupted coarsening in which an ordered cell pattern develops with constant wavelength and amplitude at intermediate distances, while the profile is disordered and rough at larger distances. Moreover, for a wide range of parameters the lateral extent of ordered domains ranges up to tens of cells. This behavior is new in the context of dynamics of surfaces or interfaces with morphological instabilities. We also provide analytical estimates for the stationary pattern wavelength and mean growth velocity

Integrable open-boundary conditions for the supersymmetric t-J model. The quantum group invariant case

We consider integrable open--boundary conditions for the supersymmetric t--J model commuting with the number operator $n$ and $S^{z}$. Four families, each one depending on two arbitrary parameters, are found. We find the relation between Sklyanin's method of constructing open boundary conditions and the one for the quantum group invariant case based on Markov traces. The eigenvalue problem is solved for the new cases by generalizing the Nested Algebraic Bethe ansatz of the quantum group invariant case (which is obtained as a special limit). For the quantum group invariant case the Bethe ansatz states are shown to be highest weights of $spl_{q}(2,1)$.Comment: Latex, 24 pages. Some new comments and references. Final version to appear in Nucl. Phys.

Anomalous scaling in a non local growth model in the Kardar-Parisi-Zhang universality class

We study the interface dynamics of a discrete model to quantitatively describe electrochemical deposition experiments. Extensive numerical simulations indicate that the interface dynamics is unstable at early times, but asymptotically displays the scaling of the Kardar-Parisi-Zhang universality class. During the time interval in which the surface is unstable, its power spectrum is anomalous; hence the behaviors at length scales smaller than or comparable with the system size are described by different roughness exponents. These results are expected to apply to a wide range of electrochemical deposition experiments.Comment: REVTEX (4 pages) and three figures (postscript), to be published in PRE (rapid communication, March, 1998