Infrared dynamics in (2+1) dimensions

In this work we study the asymptotic behavior of (2+1)-dimensional quantum electrodynamics in the infrared region. We show that an appropriate redefinition of the fermion current operator leads to an asymptotic evolution operator that contains a divergent Coulomb phase factor and a contribution from the electromagnetic field at large distances, factored from the evolution operator for free fields, and we conclude that the modified scattering operator maps two spaces of coherent states of the electromagnetic field, as in the Kulish-Faddeev model for QED (quantum electrodynamics) in four space-time dimensions.

Bose-Einstein condensation dynamics in three dimensions by the pseudospectral and finite-difference methods

We suggest a pseudospectral method for solving the three-dimensional time-dependent Gross-Pitaevskii (GP) equation, and use it to study the resonance dynamics of a trapped Bose-Einstein condensate induced by a periodic variation in the atomic scattering length. When the frequency of oscillation of the scattering length is an even multiple of one of the trapping frequencies along the x, y or z direction, the corresponding size of the condensate executes resonant oscillation. Using the concept of the differentiation matrix, the partial-differential GP equation is reduced to a set of coupled ordinary differential equations, which is solved by a fourth-order adaptive step-size control Runge-Kutta method. The pseudospectral method is contrasted with the finite-difference method for the same problem, where the time evolution is performed by the Crank-Nicholson algorithm. The latter method is illustrated to be more suitable for a three-dimensional standing-wave optical-lattice trapping potential.

Quantum discrete phase space dynamics and its continuous limit

The main aspects of a discrete phase space formalism are presented and the discrete dynamical bracket, suitable for the description of time evolution in finite-dimensional spaces, is discussed. A set of operator bases is defined in such a way that the Weyl-Wigner formalism is shown to be obtained as a limiting case. In the same form, the Moyal bracket is shown to be the limiting case of the discrete dynamical bracket. The dynamics in quantum discrete phase spaces is shown not to be attained from discretization of the continuous case.

Short-time dynamics of percolation observables

We consider the critical short-time evolution of magnetic and droplet-percolation order parameters for the Ising model in two and three dimensions, through Monte Carlo simulations with the (local) heat-bath method. We find qualitatively different dynamic behaviors for the two types of order parameters. More precisely, we find that the percolation order parameter does not have a power-law behavior as encountered for the magnetization, but develops a scale (related to the relaxation time to equilibrium) in the Monte Carlo time. We argue that this difference is due to the difficulty in forming large clusters at the early stages of the evolution. Our results show that, although the descriptions in terms of magnetic and percolation order parameters may be equivalent in the equilibrium regime, greater care must be taken to interpret percolation observables at short times. In particular, this concerns the attempts to describe the dynamics of the deconfinement phase transition in QCD using cluster observables.

Bose-Einstein condensation dynamics from the numerical solution of the Gross-Pitaevskii equation

We study certain stationary and time-evolution problems of trapped Bose-Einstein condensates using the numerical solution of the Gross-Pitaevskii (GP) equation with both spherical and axial symmetries. We consider time-evolution problems initiated by suddenly changing the interatomic scattering length or harmonic trapping potential in a stationary condensate. These changes introduce oscillations in the condensate which are studied in detail. We use a time iterative split-step method for the solution of the time-dependent GP equation, where all nonlinear and linear non-derivative terms are treated separately from the time propagation with the kinetic energy terms. Even for an arbitrarily strong nonlinear term this leads to extremely accurate and stable results after millions of time iterations of the original equation.

PRODUCTION of THERMAL PHOTONS IN VISCOUS FLUID DYNAMICS WITH TEMPERATURE-DEPENDENT SHEAR VISCOSITY

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Numerical approximation of the Ginzburg-Landau equation with memory effects in the dynamics of phase transitions

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Shear viscosity from thermal fluctuations in relativistic conformal fluid dynamics

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Noise and ultraviolet divergences in the dynamics of the chiral condensate in QCD

The time evolution of the matter produced in high energy heavy-ion collisions seems to be well described by relativistic viscous hydrodynamics. In addition to the hydrodynamic degrees of freedom related to energy-momentum conservation, degrees of freedom associated with order parameters of broken continuous symmetries must be considered because they are all coupled to each other. of particular interest is the coupling of degrees of freedom associated with the chiral symmetry of QCD. Quantum and thermal fluctuations of the chiral fields act as noise sources in the classical equations of motion, turning them into stochastic differential equations in the form of Ginzburg-Landau-Langevin (GLL) equations. Analytic solutions of GLL equations are attainable only in very special circumstances and extensive numerical simulations are necessary, usually by discretizing the equations on a spatial lattice. However, a not much appreciated issue in the numerical simulations of GLL equations is that ultraviolet divergences in the form of lattice-spacing dependence plague the solutions. The divergences are related to the well-known Rayleigh-Jeans catastrophe in classical field theory. In the present communication we present a systematic lattice renormalization method to control the catastrophe. We discuss the implementation of the method for a GLL equation derived in the context of a model for the QCD chiral phase transition and consider the nonequilibrium evolution of the chiral condensate during the hydrodynamic flow of the quark-gluon plasma.

Langevin dynamics of the deconfinement transition for pure gauge theory

We investigate the effects of dissipation in the deconfinement transition for pure SU(2) and SU(3) gauge theories. Using an effective theory for the order parameter, we study its Langevin evolution numerically. Noise effects are included for the case of SU(2). We find that both dissipation and noise have dramatic effects on the spinodal decomposition of the order parameter and delay considerably its thermalization. For SU(3) the effects of dissipation are even larger than for SU(2).

Dynamics of Enceladus and Dione inside the 2:1 mean-motion resonance under tidal dissipation

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Tectonic history and the biogeography of the freshwater fishes from the coastal drainages of eastern Brazil: an example of faunal evolution associated with a divergent continental margin

As drenagens costeiras do leste do Brasil correspondem a áreas de grande significado biogeográfico, apresentando um alto grau de endemismo em sua fauna de peixes. Padrões filogenéticos sugerem uma relação próxima entre os rios que correm para o Atlântico a os adjacentes das terras altas do escudo cristalino. Entretanto, pouco tem sido dito sobre a dinâmica dos processos geológicos relacionados aos eventos cladogenéticos entre estas áreas. Padrões de distribuição e filogenéticos sugerem uma íntima associação com a história geológica da margem continental passiva da América do Sul, desde o Cretáceo aos dias atuais. Soerguimentos macrodômicos, rifteamento, movimentos verticais entre blocos falhados e o recuo erosivo da margem leste sul-americana são considerados como as principais forças geológicas atuando sobre a distribuição da ictiofauna de água doce nestas áreas. A atividade tectônica associada à ruptura do Gondwana e separação da América do Sul e África criou seis megadomos que são responsáveis por configurar a maior parte do atual curso das principais bacias hidrográficas do escudo cristalino. Com exceção das bacias localizadas às margens de tais megadomos, estes rios desenvolveram longos e sinuosos circuitos sobre o antigo escudo cristalino brasileiro antes de desaguarem no então recentemente aberto Oceano Atlântico. Eventos cladogenéticos iniciais entre drenagens de terras altas do escudo cristalino e tributários do Atlântico podem estar associados com processos vicariantes desta fase inicial, e alguns táxons antigos, basais, grupos-irmão de táxons muito inclusivos e de ampla distribuição são encontrados nestas bacias hidrográficas. Mais tarde, a denudação erosiva generalizada resultou em um ajuste isostático da margem leste da plataforma. Tal ajuste, concomitantemente a reativações de antigas zonas de falha, resultou em movimentos verticais entre blocos falhados, dando origem, no sudeste do Brasil, a bacias tafrogênicas. Tais bacias, como a de Taubaté, São Paulo, Curitiba e Volta Redonda, entre outras, capturaram drenagens e fauna de terras altas adjacentes. Os peixes fósseis da Formação Tremembé (Eoceno-Oligoceno da Bacia de Taubaté) exemplificam este processo. Outros sistemas tafrogênicos de idade Terciária foram também identificados em outros segmentos da margem continental Atlântica, como na Província Borborema, no NE do Brasil, com marcada influência sobre o padrão de drenagem. Ao mesmo tempo, o recuo erosivo da margem leste da plataforma capturou sucessivamente rios de planalto, os quais se tornaram tributários atlânticos, evoluindo associados aos principais sistemas de falha. A natureza continuada destes processos explica os padrões filogenéticos e de distribuição miscigenados entre os tributários atlânticos e as terras altas do escudo cristalino adjacente, especialmente na margem sudeste do continente, representados por sucessivos, cada vez menos inclusivos, grupos irmãos, associados a eventos cladogenéticos desde o final do Cretáceo ao presente.

Dynamics in discrete phase spaces and time interval operators

The von Neumann-Liouville time evolution equation is represented in a discrete quantum phase space. The mapped Liouville operator and the corresponding Wigner function are explicitly written for the problem of a magnetic moment interacting with a magnetic field and the precessing solution is found. The propagator is also discussed and a time interval operator, associated to a unitary operator which shifts the energy levels in the Zeeman spectrum, is introduced. This operator is associated to the particular dynamical process and is not the continuous parameter describing the time evolution. The pair of unitary operators which shifts the time and energy is shown to obey the Weyl-Schwinger algebra. (C) 1999 Elsevier B.V. B.V. All rights reserved.

Symmetries and time evolution in discrete phase spaces: a soluble model calculation

Using the flexibility and constructive definition of the Schwinger bases, we developed different mapping procedures to enhance different aspects of the dynamics and of the symmetries of an extended version of the two-level Lipkin model. The classical limits of the dynamics are discussed in connection with the different mappings. Discrete Wigner functions are also calculated. © 1995.

On non-ideal and non-linear portal frame dynamics analysis using Bogoliubov averaging method

We apply the Bogoliubov Averaging Method to the study of the vibrations of an elastic foundation, forced by a Non-ideal energy source. The considered model consists of a portal plane frame with quadratic nonlinearities, with internal resonance 1:2, supporting a direct current motor with limited power. The non-ideal excitation is in primary resonance in the order of one-half with the second mode frequency. The results of the averaging method, plotted in time evolution curve and phase diagrams are compared to those obtained by numerically integrating of the original differential equations. The presence of the saturation phenomenon is verified by analytical procedures.