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

Decoherence of tripartite states - a trapped ion coupled to an optical cavity

We investigate the non-dissipative decoherence of three qubit system obtained by manipulating the state of a trapped two-level ion coupled to an optical cavity. Modelling the environment as a set of noninteracting harmonic oscillators, analytical expressions for the state operator of tripartite composite system, the probability of generating maximally entangled GHZ state, and the population inversion have been obtained. The pointer observable is the energy of the isolated quantum system. Coupling to environment results in exponential decay of off diagonal matrix elements of the state operator with time as well as a phase decoherence of the component states. Numerical calculations to examine the time evolution of GHZ state generation probability and population inversion for different system environment coupling strengths are performed. Using negativity as an entanglement measure and linear entropy as a measure of mixedness, the entanglement dynamics of the tripartite system in the presence of decoherence is analysed.Comment: Revised version, errors corrected and references added. 12 pages, 6 figures, Presented at ICSSUR May 2005, Besancon, Franc

Spin-glass behaviour on random lattices

The ground-state phase diagram of an Ising spin-glass model on a random graph with an arbitrary fraction $w$ of ferromagnetic interactions is analysed in the presence of an external field. Using the replica method, and performing an analysis of stability of the replica-symmetric solution, it is shown that $w=1/2$, correponding to an unbiased spin glass, is a singular point in the phase diagram, separating a region with a spin-glass phase ($w<1/2$) from a region with spin-glass, ferromagnetic, mixed, and paramagnetic phases ($w>1/2$)

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

Micromorfologia aplicada a morfometria de agregados.

A morfometria geralmente é utilizada para análise grãos em pedologia, no entanto este trabalho teve como objetivo utilizar a técnica da micromorfologia para estudo de morfometria de agregados dos solos para que possa servir como subsídio a caracterização da estrutura do solo em escala micro. Foi realizada análise de 8 lâminas correspondente a diferentes classes de solos. Foram calculadas a porosidade e atributos morfométricos, como: área, perímetro, arredondamento, maior eixo e menor eixo utilizando o software Quantiporo. Com auxílio do Microsoft® Office Excel complementou-se os atributos alongamento e compacidade dos agregados. Em geral, os resultados de porosidade concordam com classe textural e estrutura de cada perfil, encontrando-se maior porosidade em solos mais argilosos e siltosos do que nos arenosos; isso devido a quantidade de microporos nesses solos. Encontraram-se maiores semelhanças dos atributos de solos nas classes de tamanho de agregados do que em relação as diferentes classes de solos. Mesmo sendo analisada uma parte muito pequena de solo para representar uma classe de solo, os resultados mostraram coerência, visto que, houve uma similaridade entre os perfis de mesma classe e também aqueles representando uma mesma profundidade (0-10 cm)

Semiclassical theory for small displacements

Characteristic functions contain complete information about all the moments of a classical distribution and the same holds for the Fourier transform of the Wigner function: a quantum characteristic function, or the chord function. However, knowledge of a finite number of moments does not allow for accurate determination of the chord function. For pure states this provides the overlap of the state with all its possible rigid translations (or displacements). We here present a semiclassical approximation of the chord function for large Bohr-quantized states, which is accurate right up to a caustic, beyond which the chord function becomes evanescent. It is verified to pick out blind spots, which are displacements for zero overlaps. These occur even for translations within a Planck area of the origin. We derive a simple approximation for the closest blind spots, depending on the Schroedinger covariance matrix, which is verified for Bohr-quantized states.Comment: 16 pages, 4 figures

A view of the dynamic software product line landscape

Dynamic software product lines extend the concept of conventional SPLs by enabling software-variant generation at runtime. Recent studies yield insights into the current state of the DSPL field, research trends, and major gaps to address