Nesta sexta, André, meu filho caçula defendeu tese de doutorado na Universidade de Wurzburg. Como qualquer pai babão, fiquei muito feliz. Afinal de contas meu herdeiro se doutorou num dos centros planetários mais importantes no campo da física.

Aproveito a oportunidade para cometer um exagero de pai coruja: publico aqui capa e abstract da tese do menino.

Julius-Maximilians-Universit¨at W¨urzburg

Fakult¨at f¨ur 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

W¨urzburg

W¨urzburg

2010

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 that

these 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

equilibrium. Moreover we use the same model to study fluctuation

relations. The fluctuation relation is a symmetry in the large deviation

function associated to the probability of the variation of entropy during a

fixed time interval. We argue that the entropy and height are similar

quantities within the model we consider and we calculate the Legendre

transform of the large deviation function associated to the height for small

systems. We observe that there is no fluctuation relation for the height,

nevertheless its large deviation function is still symmetric.

julho 17, 2010 às 12:00 pm |

Jarbas, parabéns para o filhão! Sucesso!

julho 17, 2010 às 12:52 pm |

Obrigado, Michel.