Lyapunov exponent for a gas of soft scatterers

For a fast particle moving within a two-dimensional array of soft scatterers - centers of weak and short-range potential - the dependence of the Lyapunov exponent on the system parameters is studied. The use of the linearized equations for variations of the propagation angles and impact parameters of consequent collisions reduces the problem to that of calculation of the Lyapunov exponent of an ensemble of strongly correlated random matrices with given statistics of matrix elements. In the simplest approximation this Lyapunov exponent is proportional to the interaction strength and inversely proportional to the square root of the interaction range. The model satisfactorily describes the intensity of chaos in a system of two weakly interacting particles moving in a two-dimensional regular confining potential.Comment: 3 pages, 3 figure

Dois mapas do padeiro acoplados e suas possíveis quantizaçoes

Orientador: Marcos G.E.da LuzApendiceTese (doutorado) - Universidade Federal do Paraná, Setor de Ciencias Exatas, Curso de Pós-Graduaçao em Física. Defesa: Curitiba, 2006Inclui bibliografi

Bilhares quânticos formados por 2 partículas interagindo por potencia de curto alcance

Orientador : Marcos G. E. LuzDissertaçao (mestrado) - Universidade Federal do ParanáResumo: Neste trabalho examinamos as condições de integrabilidade e surgimento de caos em sistemas quânticos formados por duas partículas em uma dimensão. Assumimos interações de curto alcance entre as partículas e a possibilidade de existirem potenciais externos dados por funções S. Condições de contorno periódicas e do tipo paredes infinitas são consideradas. Verificamos que para surgir caos é fundamental que a razão entre os valores das massa das partículas seja diferente da unidade. Para o caso de condições de contorno periódicas mostramos que para qualquer que seja o potencial de interação de curto alcance entre as partículas a hipótese de Bethe é válida e mostramos como construir as soluções analíticas do problema neste caso. As razões dinâmicas que levam o sistema quântico a apresentar ou não caos são discutidas em detalhe.Abstract: In this work we study the integrability conditions and the emergence of chaos in quantum systems formed by two one-dimensional particles. We assume a short range interaction between the particles and also the possibility of external potentials given by S functions. Periodic boundary and hard wall boundary conditions are both considered. We find that there exists chaos only when the ratio between the particles' masses is different from unity. For the periodic boundary conditions we show that for any kind of short range interaction potential between the particles the Bethe ansatz is valid, and we also show how to construct the analytical solutions for the problem in this case. The dynamical reasons which drive the quantum system to present chaos are discussed in detail

OptiLiAna – Um aplicativo para resolução de problemas de Programação Linear

Este artigo descreve o desenvolvimento de um aplicativo para resolução de problemas de programação linear denominado OptiLiAna. O aplicativo usa o método Simplex que é um conteúdo chave para a Modelagem Matemática de problemas reais, foco da disciplina de Pesquisa Operacional (PO), ofertada no curso de Sistemas de Informação da Faculdade da Indústria – São José dos Pinhais

Gauss map and Lyapunov exponents of interacting particles in a billiard

We show that the Lyapunov exponent (LE) of periodic orbits with Lebesgue measure zero from the Gauss map can be used to determine the main qualitative behavior of the LE of a Hamiltonian system. The Hamiltonian system is a one-dimensional box with two particles interacting via a Yukawa potential and does not possess Kolmogorov-Arnold-Moser (KAM) curves. In our case the Gauss map is applied to the mass ratio $\gamma = m_2/m_1$ between particles. Besides the main qualitative behavior, some unexpected peaks in the $\gamma$ dependence of the mean LE and the appearance of 'stickness' in phase space can also be understand via LE from the Gauss map. This shows a nice example of the relation between the "instability" of the continued fraction representation of a number with the stability of non-periodic curves (no KAM curves) from the physical model. Our results also confirm the intuition that pseudo-integrable systems with more complicated invariant surfaces of the flow (higher genus) should be more unstable under perturbation.Comment: 13 pages, 2 figure

Green functions for generalized point interactions in 1D: A scattering approach

Recently, general point interactions in one dimension has been used to model a large number of different phenomena in quantum mechanics. Such potentials, however, requires some sort of regularization to lead to meaningful results. The usual ways to do so rely on technicalities which may hide important physical aspects of the problem. In this work we present a new method to calculate the exact Green functions for general point interactions in 1D. Our approach differs from previous ones because it is based only on physical quantities, namely, the scattering coefficients, $R$ and $T$, to construct $G$. Renormalization or particular mathematical prescriptions are not invoked. The simple formulation of the method makes it easy to extend to more general contexts, such as for lattices of $N$ general point interactions; on a line; on a half-line; under periodic boundary conditions; and confined in a box.Comment: Revtex, 9 pages, 3 EPS figures. To be published in PR

Dois mapas do padeiro acoplados e suas possíveis quantizaçoes

Orientador: Marcos G.E.da LuzApendiceTese (doutorado) - Universidade Federal do Paraná, Setor de Ciencias Exatas, Curso de Pós-Graduaçao em Física. Defesa: Curitiba, 2006Inclui bibliografi

Proposal Sentiment Analysis Use in Developing a new Sustainability Metrics

Sustainability metrics are measures and indicators that are intended to serve as management tools, both at the macro level, to public policy, for example, as in the micro, in the efficient management of a company. With its use one can measure the impacts of sustainable practices, through the correlation, for example, from increased revenue and market share, with practices such as reducing energy costs, reducing expenses with waste reduction costs of materials and water. Or even the correlation between an environment where Sustainability is promoted and the increased employee productivity and reduced spending on hiring. Arguably a growing alignment is needed between the discourse and practice of sustainability values. In this context, this article aims to use the Analysis of Feelings in the development of a new metric. In the present stage was done a survey, to know about the opinion that the Superior Educational Institute FAMEC - PR\u27s workers have about organizational sustentability. The answers passed by an analysis, done with the tool RapidMiner, where the workers feelings were qualified as positive, negative or neutral

APEX - The Atacama Pathfinder Experiment

APEX, the Atacama Pathfinder Experiment, has been successfully commissioned and is in operation now. This novel submillimeter telescope is located at 5107 m altitude on Llano de Chajnantor in the Chilean High Andes, on what is considered one of the world\u27s outstanding sites for submillimeter astronomy. The primary reflector with 12 m diameter has been carefully adjusted by means of holography. Its surface smoothness of 17-18 μm makes APEX suitable for observations up to 200 μm, through all atmospheric submm windows accessible from the ground