Nonequilibrium phase transitions and surface growth [Elektronische Ressource] / Andre Cardoso Barato

Sujets

• Physik

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• Publié par: julius-maximilians-universitat_wurzburg
• Publié le: 01 janvier 2010
• Nombre de lectures: 29
• Langue: English
• Poids de l'ouvrage: 2 Mo

Extrait

Julius-Maximilians-Universit¨at Wu¨rzburg
Fakult¨at fu¨r Physik und Astronomie
Nonequilibrium phase transitions and surface
growth
Andre Cardoso Barato
Betreuer: Prof. Dr. Haye Hinrichsen
Dissertation zur Erlangung des
naturwissenschaftlichen
Doktorgrades
der Julius-Maximilians-Universit¨at
Wu¨rzburg
Wu¨rzburg
2010Eingereicht am:
bei der Fakult¨at fu¨r Physik und Astronomie
1. Gutachter: Prof. Dr. H. Hinrichsen
2. Gutachter: Prof. Dr. W. Kinzel
der Dissertation.
1. Pru¨fer: Prof. Dr. H. Hinrichsen
2. Pru¨fer: Prof. Dr. W. Kinzel
3. Pru¨fer: Prof. dr. J. Geurts
im Promotionskolloquium.
Tag des Promotionskolloquiums: 16. Juli 2010
Doktorkunde ausgeh¨andigt am:Erkl¨arung an Eides Statt
Hiermit erkl¨are ich, Andre Cardoso Barato geboren am 20. April 1982 in
S˜ao Paulo, mit meiner Unterschrift an Eides Statt, dass ich die vorliegende
Arbeit selbst¨andig sowie ohne unzul¨assige Hilfe Dritter angefertigt habe
und außer den angegebenen keine weiteren Hilfsmittel zur direkten und
indirekten Erstellung dieser Arbeit (Nonequilibrium phase transitions and
surface growth) verwendet habe. S¨amtliche verwendeten Quellen befinden
sich in der Literaturangabe.
Andre Cardoso BaratoAcknowledgments
Deutsche Forschungsgemeinschaft (DFG) is gratefully acknowledge for
financial support.
For scientific collaboration I acknowledge Dietrich Wolf, Juan A Bonachela,
Carlos E Fiore, Miguel A Mun˜oz, Raphael Chetrite and David Mukamel.
I would like to thank M´ario Jos´e de Oliveira and Haye Hinrichsen for
excellent orientation during my masters and PhD, respectively. They
introduced me to nonequilibrium statistical physics.
I am thankful to my parents Ana Maria Cardoso Barato and Jarbas
Novelino Barato for many things.Abstract
This thesis is concerned with the statistical physics of various systems far
from thermal equilibrium, focusing on universal critical properties, scaling
laws and the role of fluctuations. To this end we study several models
which serve as paradigmatic examples, such as surface growth and
non-equilibrium wetting as well as phase transitions into absorbing states.
As a particular interesting example of a model with a non-conventional
scaling behavior, we study a simplified model for pulsed laser deposition by
rate equations and Monte Carlo simulations. We consider a set of
equations, where islands are assumed to be point-like, as well as an
improved one that takes the size of the islands into account. The first set of
equations is solved exactly but its predictive power is restricted to the first
few pulses. The improved set of equations is integrated numerically, is in
excellent agreement with simulations, and fully accounts for the crossover
from continuous to pulsed deposition. Moreover, we analyze the scaling of
the nucleation density and show numerical results indicating that a
previously observed logarithmic scaling does not apply.
In order to understand the impact of boundaries on critical phenomena, we
introduce particle models displaying a boundary-induced absorbing state
phase transition. These are one-dimensional systems consisting of a single
site (the boundary) where creation and annihilation of particles occur,
while particles move diffusively in the bulk. We study different versions of
these models and confirm that, except for one exactly solvable bosonic
variant exhibiting a discontinuous transition with trivial exponents, all the
others display a non-trivial behavior, with critical exponents differing from
their mean-field values, representing a universality class. We show thatthese systems are related to a (0+1)-dimensional non-Markovian model,
meaning that in nonequilibrium a phase transition can take place even in
zero dimensions, if time long-range interactions are considered. We argue
that these models constitute the simplest universality class of phase
transition into an absorbing state, because the transition is induced by the
dynamics of a single site. Moreover, this universality class has a simple field
theory, corresponding to a zero dimensional limit of direct percolation with
L´evy flights in time.
Another boundary phenomena occurs if a nonequilibrium growing interface
is exposed to a substrate, in this case a nonequilibrium wetting transition
may take place. This transition can be studied through Langevin equations
or discrete growth models. In the first case, the Kardar-Parisi-Zhang
equation, which defines a very robust universality class for nonequilibrium
moving interfaces, is combined with a soft-wall potential. While in the
second, microscopic models, in the corresponding universality class, with
evaporation and deposition of particles in the presence of hard-wall are
studied. Equilibrium wetting is related to a particular case of the problem,
corresponding to the Edwards-Wilkinson equation with a potential in the
continuum approach or to the fulfillment of detailed balance in the
microscopic models. In this thesis we present the analytical and numerical
methods used to investigate the problem and the very rich behavior that is
observed with them.
The entropy production for a Markov process with a nonequilibrium
stationary state is expected to give a quantitative measure of the distance
form equilibrium. In the final chapter of this thesis, we consider a
Kardar-Parisi-Zhang interface and investigate how entropy production
varies with the interface velocity and its dependence on the interface slope,
which are quantities that characterize how far the stationary state of the
interface is away from equilibrium. We obtain results in agreement with the
idea that the entropy production gives a measure of the distance from