Universality in Four-Boson Systems

We report recent advances on the study of universal weakly bound four-boson states from the solutions of the Faddeev-Yakubovsky equations with zero-range two-body interactions. In particular, we present the correlation between the energies of successive tetramers between two neighbor Efimov trimers and compare it to recent finite range potential model calculations. We provide further results on the large momentum structure of the tetramer wave function, where the four-body scale, introduced in the regularization procedure of the bound state equations in momentum space, is clearly manifested. The results we are presenting confirm a previous conjecture on a four-body scaling behavior, which is independent of the three-body one. We show that the correlation between the positions of two successive resonant four-boson recombination peaks are consistent with recent data, as well as with recent calculations close to the unitary limit. Systematic deviations suggest the relevance of range corrections. © 2012 Springer-Verlag.

Self-trapping of Fermi and Bose gases under spatially modulated repulsive nonlinearity and transverse confinement

We show that self-localized ground states can be created in the spin-balanced gas of fermions with repulsion between the spin components, whose strength grows from the center to periphery, in combination with the harmonic-oscillator (HO) trapping potential acting in one or two transverse directions. We also consider the ground state in the noninteracting Fermi gas under the action of the spatially growing tightness of the one- or two-dimensional (1D or 2D) HO confinement. These settings are considered in the framework of the Thomas-Fermi-von Weizsäcker (TF-vW) density functional. It is found that the vW correction to the simple TF approximation (the gradient term) is nearly negligible in all situations. The properties of the ground state under the action of the 2D and 1D HO confinement with the tightness growing in the transverse directions are investigated too for the Bose-Einstein condensate with the self-repulsive nonlinearity. © 2013 American Physical Society.

A Combined Study of the Pion's Static Properties and form Factors

We study consistently the pion's static observables and the elastic and γ* γ → π0 transition form factors within a light-front model. Consistency requires that all calculations are performed within a given model with the same and single adjusted length or mass-scale parameter of the associated pion bound-state wave function. Our results agree well with all extent data including recent Belle data on the γ* γ → π0 form factor at large q2, yet the BaBar data on this transition form factor resists a sensible comparison. We relax the initial constraint on the bound-state wave function and show the BaBar data can partially be accommodated. This, however, comes at the cost of a hard elastic form factor not in agreement with experiment. Moreover, the pion charge radius is about 40 % smaller than its experimentally determined value. It is argued that a decreasing charge radius produces an ever harder form factor with a bound-state amplitude difficultly reconcilable with soft QCD. We also discuss why vector dominance type models for the photon-quark vertex, based on analyticity and crossing symmetry, are unlikely to reproduce the litigious transition form factor data. © 2013 Springer-Verlag Wien.

Obtenção das distribuições de carga/massa e momentos no 'INTPOT. 4 HE' com o método de coordenadas geradoras

Pós-graduação em Física - IFT

Um estudo da dinâmica fracamente não-linear de um sistema nanomecânico

Pós-graduação em Matemática - IBILCE

Modelos descritos por equações diferenciais ordinárias

Pós-graduação em Matemática Universitária - IGCE

Equação de Fokker-Planck, supersimetria e enovelamento de proteína

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

Análise da potencialidade a condução do BDT através da densidade eletrônica de estados via tight binding e desenvolvimento de software (B3J)

Neste trabalho nos propomos a fazer um estudo acerca da potencialidade de condução eletrônica no polímero BDT (1,3-benzoditiol 4H-ciclopenta[2,1-b:3,4b’]). O estudo usual de polímeros conjugados é feito de modo a obter sua densidade de estados com diversos tipos e níveis de dopagem. O método de Huckel é o mais utilizado e se baseia na separabilidade das ligações sigma e pi que é possível quando a molécula estudada é plana. Os polímeros conjugados são em sua maioria planos e estão inseridos nesta aproximação. O monômero do BDT apresenta sua geometria fora do plano por apresentar ligações com orbitais sp3. Para contornar esse problema foi desenvolvido o programa B3J, que considera todos os orbitais de valencia (s, px, py e pz). O programa B3J calcula a densidade de estados de sistemas poliméricos. O estudo das bandas do BDT foi feito com este software. Calculamos a densidade de estados do sistema neutro e com diversos níveis de dopagem, com distribuição aleatória e ordenada dos defeitos, dopagem do tipo n e do tipo p. O comportamento do quadrado do coeficiente da expansão da função de onda foi obtido para polímeros de até 20 monômeros. Estes cálculos foram obtidos com geometrias dos métodos AM1 e PM3. Obtivemos os espectros de absorção de oligômeros a fim de inferir seu comportamento para um polímero. Foram utilizados cálculos de otimização de geometria através dos métodos semi-empíricos AM1 e PM3 e ZINDO/S e o método DFT. Em outro objetivo desta monografia há o estudo do aproveitamento de tetrâmeros de BDT como dispositivos eletrônicos. Tais oligômeros foram otimizados em diversos valores de potencial elétrico, com a inserção em suas cadeias de moléculas doadoras e aceitadoras para induzir um aumento no momento de dipolo da mesma.

Mecânica quântica supersimétrica: aplicações

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

O oscilador harmônico singular revisitado

The one-dimensional Schrödinger equation with the singular harmonic oscillator is investigated. The Hermiticity of the operators related to observable physical quantities is used as a criterion to show that the attractive or repulsive singular oscillator exhibits an infinite number of acceptable solutions provided the parameter responsible for the singularity is greater than a certain critical value, in disagreement with the literature. The problem for the whole line exhibits a two-fold degeneracy in the case of the singular oscillator, and the intrusion of additional solutions in the case of a nonsingular oscillator. Additionally, it is shown that the solution of the singular oscillator can not be obtained from the nonsingular oscillator via perturbation theory.

Uma abordagem teórica e experimental do oscilador harmônico em duas dimensões utilizando as curvas de Lissajous

The study of oscillatory phenomena is an important topic in several areas of knowledge. The understanding and the solution of many problems that scientists and engineers confront nowadays can be formulated, at least as an analogy, in terms of an oscillatory movement. The description of the motion of this nature has remarkable contributions to the mathematical and conceptual formation of the students and for solving daily problems in several areas. In this paper we propose a theoretical and experimental approach involving the phenomenon of harmonic oscillations in two dimensions. Lissajous curves were used as experimental demonstration of the resulting trajectories. These curves were obtained from relatively simple experimental apparatus, which is affordable in most teaching laboratories of physics.

Princípio de ação quântica de Schwinger

The Schwinger quantum action principle is a dynamic characterization of the transformation functions and is based on the algebraic structure derived from the kinematic analysis of the measurement processes at the quantum level. As such, this variational principle, allows to derive the canonical commutation relations in a consistent way. Moreover, the dynamic pictures of Schrödinger, Heisenberg and a quantum Hamilton-Jacobi equation can be derived from it. We will implement this formalism by solving simple systems such as the free particle, the quantum harmonic oscillator and the quantum forced harmonic oscillator.

Contact parameters in two dimensions for general three-body systems

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

Anderson localization and momentum-space entanglement

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

Energia eletrônica e polarizabilidade da mólecula de hidrogênio ionizada confinada

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)