Tese do André

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
Andre Cardoso Barato
Betreuer: Prof. Dr. Haye Hinrichsen
Dissertation zur Erlangung des
der Julius-Maximilians-Universit¨at

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.


2 Respostas to “Tese do André”

  1. Michel Goulart Says:

    Jarbas, parabéns para o filhão! Sucesso!

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