Made available in DSpace on 2017-07-21T19:26:00Z (GMT). No. of bitstreams: 1 JADERSANTOS.pdf: 1951823 bytes, checksum: db75a73fc3676656399742b18f6eeda8 (MD5) Previous issue date: 2011-03-18 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / The Dicke model describes a system that contain a group of atoms coupled to a mode of electromagnetic field. One of the feature of this model is the present of second order quantum phase transition. In this work our main goal is to study the quantum phase transition present in the Dicke model through a mechanical probe. We consider that one of the mirrors in a optical cavity has the freedom to move under the effect of linear restoring force. In this conditions, the mirror couples to the cavity field via pressure radiation interaction. In the thermodynamic limit, we found that the moving mirror decouples from the cavity while in the super radiant phase it suffers the action of a resulting classical force. A remarkable feature is that the entropy of the mirror is not dynamically changed in any phase when the thermodynamic limit is taken. Consequently, the mechanical system will work as a probe to study the critical reservoir namely the Dicke system. / O modelo de Dicke descreve um sistema contendo um conjunto de átomos acoplados a um modo do campo eletromagnético. Uma das características desse modelo é que ele exibe uma transição de fase quântica de segunda ordem. Neste trabalho tivemos como principal objetivo estudar a transição de fase quântica presente nesse modelo através de uma sonda mecânica. Consideramos que um dos espelhos da cavidade óptica tem liberdade para mover-se sob efeito de uma força restauradora linear. Nessas condições, o espelho livre se acopla, via interação de pressão de radiação, com o campo presente na cavidade. No limite termodinâmico observamos que na fase normal o espelho permanecerá desacoplado da cavidade, enquanto que na fase super-radiante o espelho sofre a ação de uma força clássica resultante. Uma característica importante é que a entropia do espelho não se altera dinamicamente em nenhuma das fases, quando no regime termodinâmico. Desse modo, o sistema mecânico funciona como uma sonda para estudar o reservatório (modelo de Dicke).

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Submitted by Vasti Diniz (vastijpa@hotmail.com) on 2017-09-13T14:26:30Z No. of bitstreams: 1 arquivototal.pdf: 2274734 bytes, checksum: 20f744b4f2279525b9a574a0a0de7838 (MD5) / Made available in DSpace on 2017-09-13T14:26:30Z (GMT). No. of bitstreams: 1 arquivototal.pdf: 2274734 bytes, checksum: 20f744b4f2279525b9a574a0a0de7838 (MD5) Previous issue date: 2017-02-22 / Conselho Nacional de Pesquisa e Desenvolvimento Científico e Tecnológico - CNPq / In this thesis we deal with G odel-type Universes in the context of modi ed gravity, in particular, Chern-Simons modi ed gravity and Brans-Dicke theory with cosmological constant (BD- ). The G odel-type metrics have been intensively discussed in the General Relativity (GR) over years. It is known that such a metrics present Closed Time-like Curves (CTC's), in other words, the G odel-type metrics are themselves an example of the causality violation. Our goal is verify the consistency of the G odel-type metrics within the Chern-Simons modi ed gravity in both: non-dynamical and dynamical formulations. In the non-dynamical framework, we show that is possible a vacuum solution in contrast to GR. Another essentially new result that we get is the presence of causal solutions for a well-motivated matter source, in general, the solutions have no analogue in GR. Moreover, the vacuum solution represents the limiting case separating the completely causal and non-causal regions, such a property re ects the topological features of the Chern-Simons theory. The primordial distinguishing feature between the Chern-Simons modi ed gravity and GR solutions is the presence of the breaking Lorentz symmetry. It turns out this breaking opens up a range of new solutions. We show that the non-trivial Chern-Simons solutions in the non-dynamical framework is accompanied by rst-order corrections of the Lorentz-violating parameter. Furthermore, in the dynamical framework the geometric parameters are also a ected by second-order corrections of the Lorentzviolating parameter. We also investigated the G odel-type metrics in BD- model. We obtain a vacuum solution which is completely causal, m2 = 4!2, where for ~! ! 1 one recovers the GR with a scalar eld and cosmological constant. It is worth calling attention to the role of the cosmological constant that is fundamental in this context. / Nesta tese tratamos os Universos tipo Code' no contexto da gravidade modificada, em particular, na gravidade modificada de Chern-Simons e na teoria de Brans-Dicke com constante cosmolOgica (BD-A). As metricas tipo Code' vem sendo intensamente discuti­das na Relatividade Geral (RG) ao longo dos anon. Sabe-se que tail metricas apresentam Curvas tipo Tempo Fechadas (CTC's), ou seja, as prOprias metricas tipo Code' sao um exemplo da violagao de causalidade. Nosso objetivo é verificar a consistencia das metricas do tipo Code' dentro da gravidade modificada de Chern-Simons em ambas as formula-goes: nao dinamica e dinamica. Na formulagao nao-dinamica, mostramos que é possivel uma solugao de vacuo diferentemente da RG. Outro resultado essencialmente novo que obtemos é a presenga de solugoes causais para uma fonte de materia bem motivada, em geral, as solugoes nao tem analog° na RG. Alem disso, a solugao de vacuo representa o caso limite que separa as regioes completamente causal e nao causal, tal propriedade re­flete as caracteristicas topolOgicas da teoria de Chern-Simons. A caracteristica que difere fundamentalmente as solugoes da gravidade modificada de Chern-Simons e as da RG é a presenga da quebra da simetria de Lorentz. Acontece que essa quebra abre um leque de novas solugoes. Mostramos que as solugoes nao triviais de Chern-Simons na formulagao nao dinamica sao acompanhadas por corregoes de primeira ordem do parametro de viola­gao de Lorentz. Alem disso, na formulagao dinamica os parametros geometricos tambem sao afetados por corregoes de segunda ordem do parametro de violagao de Lorentz. Investigamos tambem as metricas tipo Code' no modelo BD-A. Obtemos uma solugao de vacuo completamente causal, m2 = 4w2, onde para cD -+ oo recupera-se a GR com um campo escalar e constante cosmolOgica. Vale a pena chamar a atengao para o papel da constante cosmolOgica que é fundamental neste contexto.

This dissertation introduces some new properties of both superfluid phases of fermions with spin-orbit coupling (SOC) and superradiant phases of photons in an optical cavity. The effects of SOC on the phase transition between normal and superfluid phase are revealed; an unconventional crossover driven by SOC from the Bardeen-Cooper-Schrieffer (BCS) state to the Bose-Einstein condensate (BEC) state is verified in three different systems; and two kinds of excitations, a Goldstone mode and a Higgs mode, are demonstrated to occur in a quantum optical system. We investigate the BCS superfluid state of two-component atomic Fermi gases in the presence of three kinds of SOCs. We find that SOC drives a class of BCS to BEC crossover that is different from the conventional one without SOC. Here, we extend the concepts of the coherence length and Cooper-pair size in the absence of SOC to Fermi systems with SOC. We study the dependence of chemical potential, coherence length, and Cooper-pair size on the SOC strength and the scattering length in three dimensions (3D) (or the twobody binding energy in two dimensions (2D)) for three attractively interacting Fermi gases with 3D Rashba, 3D Weyl, and 2D Rashba SOC respectively. By adding a population imbalance to a Fermi gas with Rashba-type SOC, we also map out the finite-temperature phase diagram. Due to a competition between SOC and population imbalance, the finite-temperature phase diagram reveals a large variety of new features, including the expanding of the superfluid state regime and the shrinking of both the phase separation and the normal regimes. We find that the tricritical point moves toward a regime of low temperature, high magnetic field, and high polarization as the SOC strength increases. Besides Fermi fluids, this dissertation also gives a new angle of view on the superradiant phase in the Dicke model. Here, we demonstrate that Goldstone and Higgs modes can be observed in an optical system with only a few atoms inside a cavity. The model we study is the U(1)/Z2 Dicke model with N qubits (two-level atoms) coupled to a single photon mode.