Neste trabalho estudamos a quebra da integrabilidade no modelo fundamental de bósons com interação de contato em uma dimensão no regime repulsivo. Inicialmente, revisamos o caso integrável, onde todas as forças de interação são iguais e o modelo pode ser exatamente solucionado pelo Ansatz de Bethe. Em seguida, examinamos o caso não-integrável de diferentes interações entre cada par de átomos através do Ansatz de Jastrow. Nos concentramos no caso mais simples, onde podemos observar os efeitos da quebra da integrabilidade, a saber, o problema de três corpos. Usando o Ansatz de Jastrow, mostramos os efeitos da quebra da integrabilidade em quantidades mensuráveis, tais como a energia, funções de correlação, distribuição de momento e fator de estrutura. Algumas dessas propriedades exibem diferenças notáveis quando comparadas ao caso integrável. / In this work we study the breaking of integrability in the fundamental one-dimensional model of bosons with contact interactions in the repulsive regime. First we review the integrable case, where all interaction strengths are equal and the model can be exactly solved by the Bethe Ansatz. Then we examine the nonintegrable case of different interactions between each pair of atoms through the Jastrow Ansatz. We focus on the simplest case where we can observe the effects of broken integrability, namely the three-body problem. Using the Jastrow Ansatz, we show the effects of the breaking of integrability in some measurable quantities, such as the energy, correlation functions, momentum distribution and structure factor. Some of these properties exhibit remarkable differences compared to the integrable case.

Neste trabalho estudamos a quebra da integrabilidade no modelo fundamental de bósons com interação de contato em uma dimensão no regime repulsivo. Inicialmente, revisamos o caso integrável, onde todas as forças de interação são iguais e o modelo pode ser exatamente solucionado pelo Ansatz de Bethe. Em seguida, examinamos o caso não-integrável de diferentes interações entre cada par de átomos através do Ansatz de Jastrow. Nos concentramos no caso mais simples, onde podemos observar os efeitos da quebra da integrabilidade, a saber, o problema de três corpos. Usando o Ansatz de Jastrow, mostramos os efeitos da quebra da integrabilidade em quantidades mensuráveis, tais como a energia, funções de correlação, distribuição de momento e fator de estrutura. Algumas dessas propriedades exibem diferenças notáveis quando comparadas ao caso integrável. / In this work we study the breaking of integrability in the fundamental one-dimensional model of bosons with contact interactions in the repulsive regime. First we review the integrable case, where all interaction strengths are equal and the model can be exactly solved by the Bethe Ansatz. Then we examine the nonintegrable case of different interactions between each pair of atoms through the Jastrow Ansatz. We focus on the simplest case where we can observe the effects of broken integrability, namely the three-body problem. Using the Jastrow Ansatz, we show the effects of the breaking of integrability in some measurable quantities, such as the energy, correlation functions, momentum distribution and structure factor. Some of these properties exhibit remarkable differences compared to the integrable case.

We consider the anomalous magnetic moment of the W boson, ĸ, from an experimental and from a theoretical point of view. In the first chapter,we consider five experiments where this parameter could in principle be measured. Our results show that the W pair-production remains the best process to measure ĸ. Single W production is very sensitive to ĸ, but it is plagued by very small cross-sections. Photon-electron colliders can also be valuable for measuring ĸ through single W production. In the second chapter, we consider a composite model where ĸ is essentially free. We found that it is impossible to rule out such a model from a single measurement of ĸ. We give detailed production rates for these processes. In the second half of the thesis, we set limits on the corrections to ĸ at the one loop level; first in the minimal SM and then in a two-Higgs-doublet model. The main results are that measured corrections of 0.1 would clearly indicate non-perturbative physics while the minimal SM can accommodate corrections up to 0.02. Possible extensions of the SM cannot increase this figure by much: unless one is willing to introduce several extra weakly interacting families, it remains that 75%, or more, of the corrections will arise from the minimal SM. / Science, Faculty of / Physics and Astronomy, Department of / Graduate

The resummation of double-logarithmic perturbative contributions produced by soft- gluon radiation (Sudakov resummation) has proved to be an important tool for enlarging the applications of perturbative QCD to a wider range of kinematical regions. In particular, a complete description of W and Z boson production at high-energy hadron colliders requires the resummation of large double logarithms that dominate the transverse momentum (p(_r)) distribution at small p(_r). This can be performed either directly in transverse momentum space or in impact parameter (Fourier transform) b space. The b space method succeeds in resumming all the leading and sub-leading logarithmic terms, but does not allow a smooth transition to fixed-order dominance at high transverse momenta. In contrast, the pr space approach experiences difficulties with resumming more sub-leading logarithms. This thesis concentrates on developing the p(_r) space formalism which completely resums the first four towers of logarithms. The number of fully resummed towers is the same as for the b space method. The results are compared, both analytically and numerically, with the original b space result as well as with results of other p(_r) space methods. Parametrization of the non-perturbative effects in p(_r) space is discussed. Given recent Tevatron data on Z boson production we find good agreement between the data and the theoretical predictions. Using the same formalism, the transverse momentum distributions are also calculated for W and Z boson production at the LHC. Finally, we discuss production of like-sign W pair production in the context of double parton scattering at the LHC.

Orientador: Vicente Pleitez / Mestre

published_or_final_version / abstract / Physics / Doctoral / Doctor of Philosophy

published_or_final_version / Physics / Master / Master of Philosophy

No description available.

Mémoire numérisé par la Direction des bibliothèques de l'Université de Montréal.

In the first part of the thesis, we investigate ground state properties of Tonks-Girardeau(TG) gas in an one-dimensional periodic trap. The key issue we are interested in is whether periodically-trapped TG gas has an off-diagonal long range order. Through numerical calculations, the single-particle reduced density matrix is computed for systems with up to 265 bosons. Scaling analysis on the occupation number of the lowest orbital shows that there is no Bose-Einstein condensation for the periodically-trapped TG gas in both commensurate and incommensurate cases. We find that, for the commensurate case, the scaling exponents of the occupation number of the lowest orbital, the amplitude of the lowest orbital and the zero-momentum peak height with the particle numbers are 0, 0.5 and 1, respectively, while for the incommensurate case, they are 0.5, 0.5, and 1.5, respectively. These exponents are related to each other by a universal relation. / In the second part we study the one-dimensional "hard-sphere" fermions and bosons systems. The pair distribution functions of the one-dimensional "hard-sphere" fermions and bosons systems have been exactly evaluated by introducing gap variables. Some interesting results are obtained. Meanwhile, the pair distribution function could be measured in experiments, so hopefully our numerical results may be observed experimentally in the near future. / Lastly, we investigate the one-dimensional multi-component fermions and bosons systems. This is an extension of the work of C.N.Yang and Y.Z.You in 2011. Yang and You studied the ground state energy of w-component fermions and bosons with repulsive interactions. In this part, we investigate w-component fermions and bosons in an attractive interaction regime. Several theorems about the ground state energy of w-component fermions and bosons systems are stated and proved. Combing the results in the work of Yang and You, we finally have a comprehensive picture for the ground state energy of one-dimensional fermions and bosons systems. iii / Over the last ten years or so, there have been a number of dramatic experimental developments in trapping, cooling and controlling atoms, which open up new opportunities for studying strongly interacting many-body systems. Cold atom systems are very clean and highly tunable. Systems with different dimensionalities can be realized through optical lattice confinement, and the interactions between atoms can be fine-tuned to any value desired by Feshbach resonance. In this way various simple models can be realized to analyze subtle many-body problems which are difficult to analyze because of the complexity of the systems in real materials. / Wei, Bobo = 一維超冷原子系統中的多體物理 / 魏勃勃. / Adviser: Hai Qing Lin. / Source: Dissertation Abstracts International, Volume: 73-06, Section: B, page: . / Thesis (Ph.D.)--Chinese University of Hong Kong, 2011. / Includes bibliographical references (leaves 76-[80]). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Electronic reproduction. [Ann Arbor, MI] : ProQuest Information and Learning, [201-] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Abstract also in Chinese. / Wei, Bobo = Yi wei chao leng yuan zi xi tong zhong de duo ti wu li / Wei Bobo.