La physique statistique quantique formule les règles permettant de classifier les différentes particules. Dans cette thèse nous avons étudié deux projets, l'un portant sur les anyons dits de "Fibonacci" et l'autre sur les fermions sur réseau optique. Ici, nous avons naturellement étendu cette étude aux cas pertinent d'anyons itinérants en interaction sur des échelles. Notre but a été de construire le modèle 2D le simple possible d'anyons itinérants en interaction, analogue direct des systèmes fermioniques et inspiré par les études précédentes. En particulier, nous nous sommes demandé si la séparation spin-charge, bien connu à 1D, pouvait subsister dans le cas d'anyons sur une échelle. De plus, dans l'étude de ce modèle, nous avons découvert une nouvelle phase incompressible pouvant présenter un caractère topologique. Dans le cas des fermions confinés sur un réseau optique unidimensionnel, nous avons étudié les effets d'un chargement non-adiabatique et proposé des protocoles visant à minimiser le réchauffement du gaz quantique. Les atomes ultra-froids sur réseau optique constituent une réalisation idéale pour étudier les systèmes fortement corrélés soumis à un potentiel périodique. Le refroidissement évaporatif d'un nuage d'atomes confiné, c.a.d. sans le potentiel du réseau, s'est avéré être un processus très efficace. Les protocoles courants permettent d'obtenir(pour des fermions) des températures aussi basses que T/TF ≈ 0.08, impossible à réaliser en présence du réseau optique. Notre étude concerne les effets de redistribution de densité pour un système 1D de fermions. Notre but était de voir si des défauts causés par la mauvaise répartition des particules lors du chargement du réseau optique pouvaient empêcher les atomes de se refroidir jusqu'à la température voulue. Nous avons conçu des scenario améliorés où certains paramètres sont modifiés de façon dynamique afin de réduire la densité de défauts créés. / Quantum statistics is an important aspect of quantum mechanics and it lays down the rules for identifying dfferent classes of particles. In this thesis, we study two projects, one that surveys models of Fibonacci anyons and another that delves into fermions in optical lattices. We analyse the physics of mobile non-Abelian anyons beyond one-dimension by constructing the simplest possible model of 2D itinerant interacting anyons in close analogy to fermionic systems and inspired by the previous anyonic studies. In particular, we ask the question if spin-charge separation survives in the ladder model for non-Abelian anyons. Furthermore, in the study of this model, we have found a novel physical effective model that possibly hosts a topological gapped state. For fermions in one dimensional optical lattices, we survey the effects of non-adiabatic lattice loading on four different target states, and propose protocols to minimise heating of quantum gases. The evaporative cooling of a trapped atomic cloud, i.e. without the optical lattice potential, has been proven to be a very effective process. Current protocols are able to achieve temperatures as low as T/TF ≈ 0.08, which are lost in the presence of the optical lattice. We aim to understand if defects caused by poor distribution of particles during lattice loading are important for the fermionic case, forbidding the atoms to cool down to the desired level. We device improved ramp up schemes where we dynamically change one or more parameters of the system in order to reduce density defects.

Orientador: Marcelo Batista Hott / Banca: Denis Dalmazi / Banca: Alvaro Soares de Castro / Banca: Fabricio Augusto Barone Rangel / Banca: Humberto Belich Júnior / Resumo: Desde aproximadamente o …nal da década de 1970 efeitos quânticos e topológicos em sistemas da matéria condensada que são mostrados ocorrer a nível teórico em teoria quântica de campos têm atraído a atenção de físicos. Neste contexto, o grafeno representa uma das maiores vertentes de pesquisa dentro dos estudos das ciência dos materiais. O fato das excitações eletrônicas de baixa energia serem descritas por fermions de Dirac, estimulou uma relação frutífera entre a matéria condensada e a física de altas energias, fornecendo cenários propícios para o aparecimento de novos e exóticos fenômenos que são de grande interesse na física da matéria condensada atual. A presente tese aborda particularmente dois tópicos fundamentais da teoria quântica de campos: As Anomalias quânticas e o Fracionamento do número fermiônico. Especí…camente, estamos interessa- dos na realização de ambos fenômenos em redes de grafeno com deformações. No grafeno, um potencial vector de gauge axial surge como produto de deformações locais da rede, na forma de defeitos topológicos ou corrugações suaves. Analisaremos a in‡uência desses campos pseudomagnéticos nos estados eletrônicos para uma partícula, quando interagem com um campo magnético externo, considerando diferentes con…gurações para esses cam- pos. Estudamos o papel que desempenham os estados de modo-zero na indução de um número fermiônico fracionário e sua conexão com a anomalia de paridade / Abstract: Since approximately the late 1970s, topological quantum e¤ects in condensed mat- ter systems that are shown the occur at a theoretical level in quantum …eld theory have attracted the attention of physicists. In this context, the graphene is one of the major lines of research within the studies of materials science. The fact that the electronic exci- tations of low energy are described by Dirac fermions, stimulating a fruitful relationship between condensed matter and high energy physics, providing favorable scenarios for the arising of new and exotic phenomena which are of great interest in the current condensed- matter physics. This thesis addresses particularly two key topics of quantum …eld theory: Quantum anomalies and the fermion number fractionalization. Speci…cally, we are inter- ested in performing both phenomena in deformed graphene lattice. In graphene, an axial vector potential arises as the result of local deformations on the lattice, as topological defects or soft corrugations. We analyze the in‡uence of these pseudo-magnetic …elds on the one-particle states, when interacting with a background magnetic …eld, for di¤erents con…guration for the …elds. We study the role played by zero-mode states in fractional fermion number induced and its connection with the anomaly of parity / Doutor

Resumo: Nesta dissertação começamos estudando modelos não-lineares com campos escalares reais em (1+1) dimensões do espaço-tempo plano no âmbito da teoria supersimétrica. Analisamos as implicações da preservação da simetria Z3 no âmbito de uma teoria que preserva a supersimetria. Procuramos por um possível ladrilhamento no plano das con - gurações, plano (Á; Â), ainda com supersimetria mas com uma maior riqueza em simetrias discretas. Para isso, propusemos o superpotencial W, cuja con guração dos mínimos do potencial e os setores topológicos BPS e não-BPS, no plano (Á; Â), apresentam uma estrutura com simetria discreta complexa, na qual está contida a simetria discreta Z2­Z2. Além disso, estudamos o comportamento das soluções topológicas através da variação dos valores de um parâmetro c0 associado à equação da órbita. Também estudamos modelos não-lineares com campos escalares reais acoplados à gravidade em (4+1) dimensões do espaço-tempo deformado. Consideramos alguns modelos que geram branas espessas (defeitos topológicos) onde a gravidade pode ser localizada. Nós achamos o valor da energia do campo escalar para todo modelo que gera brana espessa. Também estudamos a energia do sistema e sua relação com as equações de Bogomol'nyi e as Equações de Einstein. Finalmente, ampliamos a análise de um modelo com dinâmica não-canônica no cenário de mundos-brana. Neste caso, constatamos que, embora o modelo possuí uma dinâmica não-canônica, ele admite branas espessas que suportam localização de férmions sem massa / Abstract: In this dissertation we begin by studying non-linear models with real scalar elds in (1+1) dimensions of a space-time. Such models can be seen as the bosonic sector of a supersymmetric theory. We analyze the implications of the Z3 symmetry under a theory that preserves supersymmetry. We look for the necessary conditions to tile the con guration plane (Á; Â), by keeping the supersymmetry together with a great wealth of discrete symmetries. For this, we propose a superpotential W, whose con guration of minima of the potential and topological BPS and non-BPS solutions have a complex structure with discrete symmetry, as the Z2 ­ Z2 symmetry. Furthermore, we study the behavior of solutions of the equations by means of the orbit equation. Moreover, we study non-linear models with real scalar elds coupled to gravity in (4+1) dimensions. We consider some models that generate thick branes (topological defects) where gravity can be localized. We analyze the implications of the metric AdS5 and the minimum of the energy associated to the scalar elds, particularly in the region of the extra space coordinate where the energy density of matter is negative. We also study the energy of the system and its relationship to Bogomol'nyi and Einstein equations. Finally, we nish the analysis of thick branes in warped space-time by introducing a model which engenders a generalized dynamics for the scalar eld. We show that despite the non-canonical dynamics, such models engenders thick branes which can support localized massless fermions / Orientador: Marcelo Batista Hott / Coorientador: Alvaro de Souza Dutra / Banca: Julio Marny Hoff da Silva / Banca: Carlos Alberto Santos Almeida / Mestre

Thesis (MSc)--Stellenbosch University, 2004. / ENGLISH ABSTRACT: In this thesis, generalized Dyson boson-fermion mappings are considered. These are techniques used in the analysis of the quantum many-body problem, and are instances of so-called boson expansion methods. A generalized Dyson boson-fermion mapping, or a Dyson mapping for short, is a one-to-one linear but non-unitary operator that can be applied to vectors representing the states of a many-fermion system. A vector representing a fermion system maps onto a vector that is most naturally interpreted as representing a state of a many-body system that contains both bosons and fermions. The motivation for doing such a mapping is the hope that the mapping will reveal some property of the system that simplifies its analysis and that was hidden in the original form. The aims of this thesis are 1. to review the theory of generalized Dyson boson-fermion mappings, 2. by considering a tutorial example, to demonstrate that it is feasible to implement the theory and 3. to find a useful application for a generalized Dyson boson-fermion mapping, by considering a non-trivial model, namely the Richardson model for superconductivity. The realization of the first two aims mainly involve the collecting together of ideas that have already appeared in the literature, into one coherent text. Some subtle points that were treated only briefly due to space restrictions in the journal publications where the theory was first expounded, are elaborated on in the present work. On the other hand, the analysis of the Richardson Hamiltonian that uses a Dyson mapping, goes beyond what has already appeared in the literature. It is the first time that a boson expansion technique is implemented for a system where the roles of both collective and non-collective fermion pairs are important. (The Dyson mapping associates bosons with Cooper pairs, while the fermions not bound in Cooper pairs result in fermions being present in the mapped system as well.) What is found is that the Dyson mapping uncovers non-trivial properties of the system. These properties aid the construction of time-independent perturbation expansions for the stationary states of the system, as well as time-dependent expansions for transition amplitudes between states. The time-independent expansions agree with results that other authors obtained through methods other than boson expansions. The time-dependent expansions, that one would be hard-pressed to develop without a Dyson mapping, might in future prove useful in understanding aspects of the dynamics of ultracold fermi gases, when time-dependent magnetic fields are used to vary the atom-atom interaction strenght. / AFRIKAANSE OPSOMMING: In hierdie tesis word veralgemeende Dyson boson-fermion-afbeeldings ondersoek. Hierdie afbeeldings word gebruik in die analise van die kwantum veeldeeltjie probleem, en is voorbeelde van sogenaamde boson-uitbreidingstegnieke. 'n Veralgemeende Dyson bosonfermion- afbeelding, of kortweg 'n Dyson afbeelding, is 'n een-tot-een, lineêre maar nie-unitêre operator wat inwerk op vektore wat toestande verteenwoordig van 'n veel-fermion sisteem. 'n Vektor wat 'n fermionsisteem verteenwoordig word so afgebeeld op 'n vektor waarvoor die mees natuurlike interpretasie is dat dit 'n toestand verteenwoordig van 'n sisteem waarin beide bosone en fermione aanwesig is. So 'n afbeelding word gewoonlik gemaak in die hoop dat eienskappe van die sisteem, wat versteek was in die oorspronklike weergawe, voor-die-hand-liggend is na die afbeelding. Hierdie tesis het ten doel 1. om die teorie van veralgemeende Dyson boson-fermion-afbeeldings te hersien, 2. om 'n eenvoudige voorbeeld deur te werk, en so te demonstreer dat die teorie sonder moeite geïmplimenteer kan word en 3. om 'n nuttige toepassing te vind vir 'n veralgemeende Dyson boson-fermion-afbeelding deur 'n nie-triviale model, naamlik die Richardson model vir supergeleiding, te ondersoek. Die eerste twee van hierdie doelwitte behels hoofsaaklik dat idees wat reeds in die literatuur verskyn het, saamgevat word in een koherente teks. Sommige subtiele punte wat, vanwee beperkte ruimte, slegs kortliks bespreek is in die joernaalartikels waarin die teorie oorspronklik verskyn het, word in hierdie tesis meer breedvoering bespreek. Daarteenoor verteenwoordig die analise van die Richardson model met behulp van 'n Dyson afbeelding 'n nuwe bydra. Dit is naamlik die eerste keer dat 'n bosonuitbreiding ingespan word vir 'n sisteem waar sowel kollektiewe as nie-kollektiewe fermionpare 'n belangrike rol speel. (Die Dyson afbeelding assosieer bosone met die oorspronklike sisteem se Cooper pare, terwyl die fermione wat in die oorspronklike sisteem nie tot Cooper pare gebind is nie, sorg dat daar ook fermione teenwoordig is in die afgebeelde sisteem.) Ons vind dat die Dyson afbeelding nie-triviale eienskappe van die sisteem aan die lig bring. Hierdie eienskappe is nuttig vir die konstruksie van beide tyd-onafhanklike steuringsreekse vir die stasionêre toestande van die sisteem en vir tyd-afhanklike steuringsreekse vir oorgangsamplitudes tussen toestande. Die tyd-onafhanklike uitbreidings stem ooreen met resultate wat ander outeurs afgelei het sonder die gebruik van 'n Dyson afbeelding. Die tyd-afhanklike uitbreidings, wat kwalik afgelei kan word sonder 'n Dyson afbeelding, mag vorentoe nuttig wees om aspekte van die dinamika van baie koue Fermi gasse te verstaan, wanneer tydafhanklike magneetvelde gebruik word om die inter-atoomwisselwerking te manipuleer.

Thesis (MSc)--Stellenbosch University, 2014. / ENGLISH ABSTRACT: We present a theoretical approach that allows for the description of trapped Bose-Fermi mixtures with a tunable interspecies interaction in the vicinity of a Feshbach resonance magnetic field.The many-body physics of the system is treated at equilibrium using the well-established mean-field and local density approximations. This reduces the physics locally to that of a homogeneous system. We observe a rich local phase structure exhibiting both first and second order phase transitions between the normal and BEC phases. We also consider the global properties of the mixture at a fixed number of particles and investigate how the density profiles and the populations of the various particle species depend on the detuning and trap profile. / AFRIKAANSE OPSOMMING: Ons beskou ’n teoretiese beskrywing van gevangde Bose-Fermi mengsels met ’n verstelbare interspesie wisselwerking in die teenwoordigheid van ’n magneties-geïnduseerde Feshbach resonansie. Die veeldeeltjiefisika van die sisteem word by ekwilibrium binne die welbekende gemiddelde-veld en lokale-digtheid benaderings hanteer. Sodoende word die fisika lokaal tot die van ’n homogene sisteem gereduseer. Ons neem ’n ryk fase-struktuur waar met beide eerste- en tweede-orde fase-oorgange tussen die normale en BEK fases. Ons beskou ook die globale eienskappe van die mengsel by ’n vaste totale aantal deeltjies en ondersoek hoe die digtheidsprofiele en deeltjiegetalle van die afstemming en die profiel van die val afhang.

This thesis presents a study of two-dimensional electron systems in GaAs-(Al,Ga)As heterojunctions and quasi-two-dimensional electron and hole systems in graphite within the quantum Hall effect regime of low temperature and high magnetic field. This thesis covers three main sets of experimental work as well as details of the experimental methods (chapter 2) used and the background theory behind the observed results (chapter 1). The first experimental results presented in this thesis in chapter 3 focus on contactless measurement of the equilibrium magnetisation of sample A2268, a ten layer multiple quantum well sample. Fitting the shape of dHvA oscillations at various temperatures to different models for the density of states, various properties of the system can be estimated, such as the shape of the disorder-broadened density of states and the presence of a background density of states between the Landau levels. Chapter 4 focuses on measurements of the decay of induced circulating currents in the quasi-dissipationless quantum Hall regime in two samples, V0049 and T73. The induced current is measured via contactless measurement of the associated magnetic moment. The magnitude of the induced current is found to be affected by the sweep rate of the magnetic field and also the distance of approach. The decay of the induced currents is observed at several temperatures and for different magnetic field sweep rates and distances of approach. Decays are observed for up to several days at time, far longer than previously possible. Information about the rate of decay can be used to build a picture of the decay mechanisms present in the quantum Hall regime. The presence of a power-law decay regime indicates many decay mechanisms contribute to the decay of a circulating current in the quasi-dissipationless quantum Hall regime. Chapter 5 focuses on both contactless magnetometry and transport experiments carried out on a graphite sample. The experiments aim to confirm or dispute recent claims of Dirac fermions in graphite. Experiments are carried out at temperatures in the range 30 mK to ~4 K and at two different angles to the applied magnetic field. Phase analysis of both Shubnikov de Haas and de Haas van Alphen oscillations is used to distinguish between normal and Dirac fermions. Observation of quantum Hall effect displays the presence of a half-integer quantum Hall staircase similar to that observed in graphene.

Deng Shusa = 费米系統中的量子纠缠 : 在一维哈伯德模型中的研究 / 邓蜀萨. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2005. / Includes bibliographical references (leaves 85-90). / Text in English; abstracts in English and Chinese. / Deng Shusa = Feimi xi tong zhong de liang zi jiu chan : zai yi wei Habode mo xing zhong de yan jiu / Deng Shusa. / Abstract --- p.i / Acknowledgement --- p.iii / Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- Motivation --- p.1 / Chapter 1.2 --- Introduction to our study on quantum entanglement --- p.2 / Chapter 1.3 --- Introduction to Quantum Entanglement --- p.3 / Chapter 1.4 --- Introduction to Quantum Phase Transition --- p.7 / Chapter 1.5 --- Introduction to Extended Hubbard Model --- p.9 / Chapter 1.6 --- Arrangement of thesis writing --- p.14 / Chapter 2 --- Measurements of Entanglement --- p.15 / Chapter 2.1 --- Von neumann entropy --- p.16 / Chapter 2.2 --- Concurrence --- p.20 / Chapter 2.3 --- Negativity --- p.22 / Chapter 2.4 --- Other measurements --- p.24 / Chapter 3 --- Fermionic concurrence --- p.26 / Chapter 3.1 --- The model and formulism --- p.27 / Chapter 3.2 --- Extended Hubbard dimer with two electrons --- p.31 / Chapter 3.3 --- Dimer under a nonuniform field --- p.38 / Chapter 3.4 --- Large system for site=6 --- p.41 / Chapter 3.5 --- Negativity --- p.44 / Chapter 4 --- Block Entanglement --- p.48 / Chapter 4.1 --- The model and formulism --- p.50 / Chapter 4.2 --- Three-dimensional Phase diagram --- p.55 / Chapter 4.3 --- Entanglement change with block size and parameter --- p.62 / Chapter 4.4 --- Entanglement change with size and parameter --- p.66 / Chapter 4.5 --- Scaling behavior for block block entanglement --- p.70 / Chapter 4.6 --- Further discussion --- p.73 / Chapter 5 --- Conclusion --- p.82 / Bibliography --- p.85

Lu, Wenlong = 一维光格子中费米型原子混合物基态行为的玻色化研究 / 魯文龙. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2009. / Includes bibliographical references (p. 70-72). / Abstract also in Chinese. / Lu, Wenlong = Yi wei guang ge zi zhong Feimi xing yuan zi hun he wu ji tai xing wei de Bose hua yan jiu / Lu Wenlong. / Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- Cold-atom systems --- p.1 / Chapter 1.1.1 --- Optical lattices --- p.2 / Chapter 1.1.2 --- Feshbach resonance --- p.3 / Chapter 1.2 --- Outline of the thesis --- p.6 / Chapter 2 --- Bosonization method --- p.8 / Chapter 2.1 --- Special property of one-dimensional Fermion system --- p.9 / Chapter 2.2 --- Bosonization techniques --- p.13 / Chapter 2.2.1 --- Density operators as bosonic fields --- p.14 / Chapter 2.2.2 --- Bosonization Identities --- p.17 / Chapter 2.3 --- Renormalization analysis for Sine-Gordon field --- p.19 / Chapter 2.4 --- Summary --- p.25 / Chapter 3 --- Mass imbalance in the spin polarized fermion system --- p.26 / Chapter 3.1 --- Kinetic term --- p.29 / Chapter 3.2 --- Interaction term --- p.32 / Chapter 3.3 --- Phase separation --- p.38 / Chapter 3.4 --- Dominant order and pairing behavior --- p.47 / Chapter 3.5 --- Summary --- p.49 / Chapter 4 --- Mass imbalance in the strong repulsive interaction region --- p.50 / Chapter 4.1 --- Effective Hamiltonian at large U limit --- p.50 / Chapter 4.2 --- Bosonization of t-J-Jz model --- p.54 / Chapter 4.3 --- Phase separation --- p.60 / Chapter 4.4 --- Summary --- p.67 / Chapter 5 --- Conclusions --- p.68 / Bibliography --- p.70 / Chapter A --- Proofs of Bosonization --- p.73 / Chapter A.1 --- Anti-commutation relations between two branches of fermionic field operators --- p.73 / Chapter A.2 --- Bosonization-identities checking --- p.74 / Chapter B --- Diagonalization of Quadratic Hamiltonian with Two Bosonic Fields --- p.77 / Chapter C --- Correlation functions --- p.82

Chung, Chun Kit = 超低溫相互作用費米原子中配對的探究 / 鍾俊傑. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2010. / Includes bibliographical references (leaves 81-88). / Abstracts in English and Chinese. / Chung, Chun Kit = Chao di wen xiang hu zuo yong fei mi yuan zi zhong pei dui de tan jiu / Zhong Junjie. / Chapter 1 --- Introduction --- p.1 / Chapter 2 --- Review on BCS theory --- p.4 / Chapter 2.1 --- BCS theory in uniform systems --- p.4 / Chapter 2.1.1 --- Hamiltonian and ground state solutions --- p.4 / Chapter 2.1.2 --- Choice of interaction potential --- p.7 / Chapter 2.1.3 --- Uniform atomic gas at T = 0 --- p.9 / Chapter 2.2 --- Self-consistent field method --- p.13 / Chapter 2.2.1 --- Population imbalanced systems --- p.17 / Chapter 2.3 --- Description of BCS states at finite temperatures --- p.22 / Chapter 3 --- Bipartite quantum entanglement in BCS states --- p.25 / Chapter 3.1 --- Mixed state bipartite quantum entanglement --- p.26 / Chapter 3.1.1 --- PPT criterion --- p.27 / Chapter 3.1.2 --- Negativity of p --- p.28 / Chapter 3.1.3 --- Entanglement witness --- p.30 / Chapter 3.1.4 --- Two-particle density matrix and two-body negativity --- p.30 / Chapter 3.2 --- Opposite spin states as subsystems --- p.31 / Chapter 3.2.1 --- Structure of and the negativity --- p.32 / Chapter 3.2.2 --- Relationship between the negativity and the order pa- rameter --- p.33 / Chapter 3.2.3 --- Distribution of negative eigenvalues of --- p.34 / Chapter 3.2.4 --- Constructing entanglement witness operator --- p.35 / Chapter 3.2.5 --- Remark: Same spin state as subsystems --- p.37 / Chapter 3.3 --- Momentum states as subsystems --- p.40 / Chapter 3.3.1 --- A and B as opposite momentum states --- p.41 / Chapter 3.3.2 --- A and B as different momentum states k and k' with k≠± k' --- p.43 / Chapter 3.3.3 --- A and B as the same momentum state --- p.44 / Chapter 3.4 --- Summary --- p.45 / Chapter 4 --- Radio-frequency spectroscopy --- p.47 / Chapter 4.1 --- The model Hamiltonian and dynamical equations --- p.49 / Chapter 4.1.1 --- Time-dependent variational method --- p.50 / Chapter 4.1.2 --- Time-dependent Bogoliubov-de Gennes equations --- p.51 / Chapter 4.2 --- Short-time dynamics --- p.53 / Chapter 4.2.1 --- Eigenvectors and Eigenvalues of C --- p.54 / Chapter 4.2.2 --- Build up of particle number density n3 and order param- eter Δ23 --- p.57 / Chapter 4.3 --- Summary --- p.61 / Chapter 5 --- Pairing in three-component systems --- p.63 / Chapter 5.1 --- The mean-field Hamiltonian --- p.64 / Chapter 5.2 --- Symmetric systems --- p.67 / Chapter 5.2.1 --- Quasiparticle spectra --- p.68 / Chapter 5.2.2 --- "Occupation number, condensation amplitude, and co- herence amplitude" --- p.70 / Chapter 5.2.3 --- Strengths of Ω --- p.71 / Chapter 5.3 --- Pairing in asymmetric systems --- p.73 / Chapter 5.3.1 --- Quasiparticle spectra and mean-field solutions --- p.73 / Chapter 5.3.2 --- Effects of Ωij --- p.74 / Chapter 5.4 --- Summary --- p.76 / Chapter 6 --- Conclusion and outlook --- p.79 / Bibliography --- p.81 / Chapter A --- Regularization techniques --- p.89 / Chapter B --- Wick's theorem --- p.91 / Chapter C --- Analytic solutions to three-component symmetric systems --- p.94

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