We are developing theoretical and computational methods to study two related three-body processes in ultracold quantum gases: three-body resonances and three-body recombination. Three-body recombination causes the ultracold gas to heat up and atoms to leave the trap where they are confined. Therefore, it is an undesirable effect in the process of forming ultracold quantum gases. Metastable three-body states (resonances) are formed in the ultracold gas. When decaying they also give additional kinetic energy to the gas, that leads to the heating too. In addition, a reliable method to obtain three-body resonances would be useful in a number of problems in other fields of physics, for example, in models of metastable nuclei or to study dissociative recombination of H3 +. Our project consists of employing computer modeling to develop a method to obtain three-body resonances. The method uses a novel two-step diagonalization approach to solve the three-body Schrödinger equation. The approach employs the SVD method of Tolstikhin et al. coupled with a complex absorbing potential. We tested this method on a model system of three identical bosons with nucleon mass and compared it to the results of a previous study. This model can be employed to understand the 3He nucleus . We found one three-body bound state and four resonances. We are also studying Efimov resonances using a 4He-based model. In a system of identical spinless bosons, Efimov states are a series of loosely bound three-body states which begin to appear as the energy of the two-body bound state approaches zero . Although they were predicted 35 years ago, recent evidence of Efimov states found by Kraemer et al. in a gas of ultracold Cs atoms has sparked great interest by theorists and experimentalists. Efimov resonances are a kind of pre-dissociated Efimov trimer. To search for Efimov resonances we tune the diatom interaction potential, V(r): V(r) → λV(r) as Esry et al. did . We calculated the first two values of λ for which there is a "condensation" (infinite number) of Efimov states. They are λEfimov1 = 0.9765 and λEfimov2 = 6.834. We performed calculations for λ = 2.4, but found no evidence of Efimov resonances. For future work we plan to work with λ ≈ 4 and λ ≈ λEfimov2 where we might see d-wave and higher l-wave Efimov resonances. There is also a many-body project that forms part of this thesis and consists of a direct diagonalization of the Bogolyubov Hamiltonian, which describes elementary excitations of a gas of bosons interacting through a pairwise interaction. We would like to reproduce the corresponding energy spectrum. So far we have performed several convergence tests, but have not observed the desired energy spectrum. We show preliminary results.

Submitted by Maicon Juliano Schmidt (maicons) on 2015-04-16T19:19:32Z No. of bitstreams: 1 Daiana Felix Pereira.pdf: 18723332 bytes, checksum: 89418a1724c3f8df1ec40b4f29a83b26 (MD5) / Made available in DSpace on 2015-04-16T19:19:32Z (GMT). No. of bitstreams: 1 Daiana Felix Pereira.pdf: 18723332 bytes, checksum: 89418a1724c3f8df1ec40b4f29a83b26 (MD5) Previous issue date: 2012-01-31 / Nenhuma / Esse trabalho investiga o processo de educar a voz de bailarinos contemporâneos por meio da educação corporal e vocal. Problematiza a questão vocal e busca entender o ensino da dança e da música que, historicamente desmembrou o corpo de quem aprende. Relaciona a essa problematização à formação na dança contemporânea com todos os desafios relacionados à manutenção da dominação masculina. Reconstrói a trajetória histórica da dança, entrelaçando-a com questões de gênero que trazem alguns conceitos como: a educação do corpo como processo do movimento e as questões da sexualidade interpretadas na dança como sentimentos eróticos. Além desse estudo teórico, a dissertação compõe dois ensaios: o primeiro inaugura um entre-ato por meio de uma análise sobre o V capítulo da obra de Rousseau (1712- 1778), "Emílio ou Da Educação, propondo uma possível dança entre Emílio e Sofia. E o segundo ensaio diz respeito a gravação com bailarinas e cantores exercitando o uso do corpo e da voz simultaneamente a fim de perceber os processos implicados nessa articulação. A dissertação aponta para uma nova linguagem e uma pedagogia da união entre a dança e a voz: artes essencialmente do corpo. É possível uma união entre as duas artes, destacando a questão da voz, bem como as questões do corpo como um todo. / This work investigates the process of educating the voice of contemporary dancers through vocal and body movement education. It seeks to understand how teaching dance and music historically disassociate itself from the body of the learner. Related to this question of contemporary dance training methods is also the question of gender roles and in particular that of male dominance. This thesis examines the historical trajectory of dance, weaving in issues of gender in relation to concepts such as education of the body, and the process of movement, as well as the topic of sexuality and how dance is often interpreted in terns of erotic feelings. This theoretical study looks at two essays in depth: the first is an analysis of Rousseau’s Chapter V (1712 - 1778), "From Emile, or Education, proposing a possible dance between Emilio and Sofia. The second essay is concerned with recording dancers and singers who train to use their body and voice simultaneously and aim to understand the processes involved that connect these two forms. This paper points to a new language and pedagogy that highlights the relationship and union between dance and voice, and the body as an art.

This thesis discusses the development and application of theoretical and computational methods to study three-body processes. The main focus is on the calculation of three-body resonances and bound states. This broadly includes the study of Efimov states and resonances, three-body shape resonances, three-body Feshbach resonances, three-body pre-dissociated states in systems with a conical intersection, and the calculation of three-body recombination rate coefficients. The method was applied to a number of systems. A chapter of the thesis is dedicated to the related study of deriving correlation diagrams for three-body states before and after a three-body collision. More specifically, the thesis discusses the calculation of the H+H+H three-body recombination rate coefficient using the developed method. Additionally, we discuss a conceptually simple and effective diabatization procedure for the calculation of pre-dissociated vibrational states for a system with a conical intersection. We apply the method to H_3, where the quantum molecular dynamics are notoriously difficult and where non-adiabatic couplings are important, and a correct description of the geometric phase associated with the diabatic representation is crucial for an accurate representation of these couplings. With our approach, we were also able to calculate Efimov-type resonances. The calculations of bound states and resonances were performed by formulating the problem in hyperspherical coordinates, and obtaining three-body eigenstates and eigen-energies by applying the hyperspherical adiabatic separation and the slow variable discretization. We employed the complex absorbing potential to calculate resonance energies and lifetimes, and introduce an uniquely defined diabatization procedure to treat X_3 molecules with a conical intersection. The proposed approach is general enough to be applied to problems in nuclear, atomic, molecular and astrophysics.