On the propagation of semiclassical Wigner functions

We establish the difference between the propagation of semiclassical Wigner functions and classical Liouville propagation. First we re-discuss the semiclassical limit for the propagator of Wigner functions, which on its own leads to their classical propagation. Then, via stationary phase evaluation of the full integral evolution equation, using the semiclassical expressions of Wigner functions, we provide the correct geometrical prescription for their semiclassical propagation. This is determined by the classical trajectories of the tips of the chords defined by the initial semiclassical Wigner function and centered on their arguments, in contrast to the Liouville propagation which is determined by the classical trajectories of the arguments themselves.Comment: 9 pages, 1 figure. To appear in J. Phys. A. This version matches the one set to print and differs from the previous one (07 Nov 2001) by the addition of two references, a few extra words of explanation and an augmented figure captio

Uniform approximation for the overlap caustic of a quantum state with its translations

The semiclassical Wigner function for a Bohr-quantized energy eigenstate is known to have a caustic along the corresponding classical closed phase space curve in the case of a single degree of freedom. Its Fourier transform, the semiclassical chord function, also has a caustic along the conjugate curve defined as the locus of diameters, i.e. the maximal chords of the original curve. If the latter is convex, so is its conjugate, resulting in a simple fold caustic. The uniform approximation through this caustic, that is here derived, describes the transition undergone by the overlap of the state with its translation, from an oscillatory regime for small chords, to evanescent overlaps, rising to a maximum near the caustic. The diameter-caustic for the Wigner function is also treated.Comment: 14 pages, 9 figure

Orbit bifurcations and the scarring of wavefunctions

We extend the semiclassical theory of scarring of quantum eigenfunctions psi_{n}(q) by classical periodic orbits to include situations where these orbits undergo generic bifurcations. It is shown that |psi_{n}(q)|^{2}, averaged locally with respect to position q and the energy spectrum E_{n}, has structure around bifurcating periodic orbits with an amplitude and length-scale whose hbar-dependence is determined by the bifurcation in question. Specifically, the amplitude scales as hbar^{alpha} and the length-scale as hbar^{w}, and values of the scar exponents, alpha and w, are computed for a variety of generic bifurcations. In each case, the scars are semiclassically wider than those associated with isolated and unstable periodic orbits; moreover, their amplitude is at least as large, and in most cases larger. In this sense, bifurcations may be said to give rise to superscars. The competition between the contributions from different bifurcations to determine the moments of the averaged eigenfunction amplitude is analysed. We argue that there is a resulting universal hbar-scaling in the semiclassical asymptotics of these moments for irregular states in systems with a mixed phase-space dynamics. Finally, a number of these predictions are illustrated by numerical computations for a family of perturbed cat maps.Comment: 24 pages, 6 Postscript figures, corrected some typo

Análise da competitividade potencial de uma cadeia de exportação de feijão.

A presente pesquisa, em andamento, apresenta como problema central de pesquisa: a cadeia de feijão para exportação é competitiva para transformar potencialidades em verdadeiras oportunidades de mercado, e o grau de competitividade indica que vale a pena direcionar esforços em organizar a cadeia produtiva de feijão para exportação

Decoherence of Semiclassical Wigner Functions

The Lindblad equation governs general markovian evolution of the density operator in an open quantum system. An expression for the rate of change of the Wigner function as a sum of integrals is one of the forms of the Weyl representation for this equation. The semiclassical description of the Wigner function in terms of chords, each with its classically defined amplitude and phase, is thus inserted in the integrals, which leads to an explicit differential equation for the Wigner function. All the Lindblad operators are assumed to be represented by smooth phase space functions corresponding to classical variables. In the case that these are real, representing hermitian operators, the semiclassical Lindblad equation can be integrated. There results a simple extension of the unitary evolution of the semiclassical Wigner function, which does not affect the phase of each chord contribution, while dampening its amplitude. This decreases exponentially, as governed by the time integral of the square difference of the Lindblad functions along the classical trajectories of both tips of each chord. The decay of the amplitudes is shown to imply diffusion in energy for initial states that are nearly pure. Projecting the Wigner function onto an orthogonal position or momentum basis, the dampening of long chords emerges as the exponential decay of off-diagonal elements of the density matrix.Comment: 23 pg, 2 fi

Scarring by homoclinic and heteroclinic orbits

In addition to the well known scarring effect of periodic orbits, we show here that homoclinic and heteroclinic orbits, which are cornerstones in the theory of classical chaos, also scar eigenfunctions of classically chaotic systems when associated closed circuits in phase space are properly quantized, thus introducing strong quantum correlations. The corresponding quantization rules are also established. This opens the door for developing computationally tractable methods to calculate eigenstates of chaotic systems.Comment: 5 pages, 4 figure

Is the droplet theory for the Ising spin glass inconsistent with replica field theory?

Symmetry arguments are used to derive a set of exact identities between irreducible vertex functions for the replica symmetric field theory of the Ising spin glass in zero magnetic field. Their range of applicability spans from mean field to short ranged systems in physical dimensions. The replica symmetric theory is unstable for d>8, just like in mean field theory. For 6<d<8 and d<6 the resummation of an infinite number of terms is necessary to settle the problem. When d<8, these Ward-like identities must be used to distinguish an Almeida-Thouless line from the replica symmetric droplet phase.Comment: 4 pages. Accepted for publication in J.Phys.A. This is the accepted version with the following minor changes: one extra sentence in the abstract; footnote 2 slightly extended; last paragraph somewhat reformulate

Desenvolvimento de sistema de consulta e visualização interativa de dados das projeções do IPCC AR4 para o Brasil.

Resumo: O objetivo deste trabalho foi desenvolver um sistema para busca e visualização de dados de variáveis climáticas projetados pelos modelos globais do Quatro Relatório (AR4) do IPCC para o Brasil. As informações são médias mensais de temperatura média, temperatura mínima, temperatura máxima, precipitação, umidade relativa e duração do período de molhamento foliar para os períodos de referência (1961-1990) e do futuro (2011-2040, 2041-2070, 2071-2100, cenários A2 e B1). O sistema iniciando com as opções do presente observado e dos cenários A2 e B1, permite uma busca por parâmetros como modelos climáticos globais, variáveis climáticas, período e mês. Os resultados das consultas são visualizados em uma grade com valores de longitude, latitude e variável climática. Com uma interface funcional, este sistema permite ao usuário a busca de dados climáticos de uma forma ágil e rápida, com apresentação dos dados organizados em um arquivo no formato ASCII (txt). Abstract: The aim of this study was to develop a system for searching and data visualization of climate variables projected by global climate models of the IPCC Fourth Assessment Report for Brazil. The variables are monthly average of mean temperature, minimum temperature, maximum temperature, precipitation, relative humidity, and duration of leaf wetness for the reference period (1961-1990) and future periods (2011-2040, 2041-2070, 2071 – 2100, A2 and B1 scenarios). The system allows the user to search for parameters, such as: global climate models, climatic variables, period, and month. The query results are displayed in a grid with values of longitude, latitude, and any climatic variable. With a functional interface, this system allows the user to search for climate data in an agile and quickly, with presentation of data in an ASCII file (txt) format

Análise de uma potencial cadeia de exportação de feijões sob a ótica da nova economia institucional.

Tem como objetivo fazer uso da Nova Economia Institucional (NEI) com ferramenta de análise das possíveis interações da cadeia produtiva do feijão para exportação.CONAFE

Mine water utilization as a secondary heat source and heat storage in a smart local heating and cooling distribution system

Mine water has been gaining increasing attention in recent years as a potential source for heat recovery and storage. This is due to its unique properties that make it an ideal medium for capturing and storing large amounts of thermal energy. Mine water is naturally heated by the earth's geothermal energy and typically has a constant temperature throughout the year, making it an excellent source of renewable energy. Additionally, the water's high thermal conductivity and large volumes provide an effective means for storing and transferring heat. With the increasing demand for sustainable energy sources and the need to reduce greenhouse gas emissions, the utilization of mine water for heat recovery and storage has become an attractive option for many industries and communities. In this project, we will explore the benefits of using mine water for heat recovery and storage, as well as some of the risks and challenges that need to be overcome to fully realize its potential as a renewable energy source