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Orientador: Gastão Inácio Krein / Banca: Maria Teresa Climaco dos Santos Thomaz / Banca: Gabriel Santos Menezes / Resumo: A presente dissertação tem como objetivo principal fazer uma revisão sobre o uso de estados coerentes para calcular a função de partição gran canônica de sistemas fermiônicos, sem empregar integrais de trajetória. Após discutir um método de cálculo baseado numa expansão de altas temperaturas, formulamos uma teoria de perturbação otimizada empregando campos auxiliares via transformação de Hubbard-Stratonovich. Aproximações não perturbativas tradicionais de campo médio tipo Hartree-Fock e de BCS são obtidas em ordem zero da teoria de perturbação otimizada. Correções não perturbativas à aproximação de ordem zero são implementadas usando uma expansão em potências de uma interação modificada, em que os efeitos dos campos médios são subtraídos da interação original do Hamiltoniano da teoria / Abstract: The primary aim of the dissertation is to review the use of coherent states for the calculation of the grand canonical partition function for fermion Systems, without employing path integrals. After discussing a calculational method based on a high temperature expansion, we formulate an optimized perturbation theory employing external fields via the Hubbard-Stratonovich transformation. Traditional non-perturbative mean field approximations like Hartree-Fock and BCS are obtained in zeroth order in the optimized perturbation theory. Non-perturbative corrections to the zeroth order approximation are implemented through a power series expansion of a modified interaction, where the effects of the mean fields are subtracted from the original interaction of the Hamiltonian of the theory / Mestre

Orientador: Vicente Pleitez / Mestre

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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.

by Chan Kwok Ming. / Chinese title in romanization: Yi wei xi tong re li xue xing zhi zhi Mengdikaluo yan jiu. / Thesis (M.Ph.)--Chinese University of Hong Kong, 1987. / Bibliography: leaf 69.

La nanostructuration de matériaux semi-conducteurs permet de modifier le comportement des porteurs de charge. Ces modifications sont causées par les effets de confinement quantique. Dans cette thèse, nous étudions par des approches théoriques (numériques et analytiques) les propriétés de réseaux cohérents de nanocristaux semi-conducteurs. Ces réseaux sont expérimentalement obtenus par des méthodes ascendantes (bottom-up) d’auto-assemblage orienté. Nous montrons que leurs structures de bandes électroniques peuvent être modélisées par un simple Hamiltonien effectif dont les énergies propres sont analytiques. En outre, nous proposons une méthode descendante (top-down) de nano-fabrication consistant en la gravure de puits quantiques semi-conducteurs par des méthodes de lithographie. Cette approche permet de reproduire artificiellement des réseaux bidimensionnels à fort intérêt et comportant des fermions de Dirac tels que le nid d’abeilles, le kagome et le Lieb. Nous étudions ensuite l’effet d’un champ magnétique statique sur un nanocristal isolé, puis sur un réseau de nanocristaux en nid d’abeilles dans lequel nous prédisons l’apparition de grands moments magnétiques. Enfin, nous montrons que dans les réseaux carrés PbSe, un désordre original portant sur les signes des termes de couplage entre nanocristaux apparaît. Nous montrons que ce désordre est réductible par des transformations de jauge, et nous quantifions le désordre réel (résiduel) ressenti par les électrons. / Semiconductor nanostructuration methods are a new route leading to the tuning of charge carriers behavior. This tuning is a direct consequence of the quantum confinement effect. In this thesis, we study using numerical and analytical approaches the properties of coherent superlattices of semiconductor nanocrystals. These superlattices are synthesized by bottom-up methods of oriented self-assembly. We show that their electronic band structures can be modeled by a simple effective Hamiltonian with analytical eigenvalues. In addition, we propose a top-down method where a periodic arrangement of holes is etched in semiconductor quantum wells using lithography. We show that it is possible to artificially reproduce two-dimensional lattices of high interest such as the honeycomb, the kagome and the Lieb lattices. Most of these lattices host Dirac fermions that we also recover in the superlattices. In another chapter, we study the effect of a static magnetic field on isolated nanocrystals and on honeycomb superlattices. We predict the presence of large magnetic moments in those systems. Finally, we show that, in PbSe square superlattices, a bond-sign disorder should arise. We find that this disorder is reducible by gauge transformations and we quantify the true (residual) disorder felt by electrons.

"October 2002" Bibliography: p. 129-136. 1. Introduction -- 2. QCD and the standard model -- 3. The Lattice -- 4. Symanzik improvement in the Static Quark Potential -- 5. Scale determination for an improved Gluon Action -- 6. Fat-link Irrelevant Clover Fermion actions -- 7. Excited Baryons in Lattice QCD -- 8. Spin 3/2 Baryons -- 9. Conclusion. This thesis reports work done in conducting numerical simulations of Lattice QCD.

"October 2002" / Bibliography: p. 129-136. / ix, 136 p. : ill. ; 30 cm. / Title page, contents and abstract only. The complete thesis in print form is available from the University Library. / This thesis reports work done in conducting numerical simulations of Lattice QCD. / Thesis (Ph.D.)--University of Adelaide, Dept. of Physics and Mathematical Physics, 2002