In the construction of Canonical Loop Quantum Gravity, General Relativity is rewritten in terms of the Ashtekar variables to simplify its quantisation. They consist of a densitised triad and a connection terms. The latter depends by definition and by construction on a free parameter β, called the Barbero–Immirzi parameter. This freedom is passed on to the quantum theory as it appears in the expressions of certain operators. Their discreet spectra depend on the arbitrary value of this parameter β, meaning that the scale of those spectra is not uniquely defined. To get around this ambiguity, we propose to consider a theory of Conformal Loop Quantum Gravity, by imposing a local conformal symmetry through the addition of a scalar field. We construct our theory starting from the usual Einstein–Hilbert action for General Relativity to which we add the action for the massless scalar field and rewrite it in terms of a new set of Ashtekar-like variables. They are constructed through a set of canonical transformations, which allow to move the Barbero–Immirzi parameter from the connection to the scalar variable. We then show that the theory can be quantised by fulfilling the conditions for a Dirac quantisation. Finally, we present some first elements of the quantum formalism. It is expected that with such a scalar-tensor theory, the quantum operators should not depend on the free parameter directly but rather on the dynamical scalar field, solving therefore the ambiguity.

by Chan Kwong Wing Raymond. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1997. / Includes bibliographical references (leaves 115-123). / Acknowledgments --- p.i / Table of Contents --- p.ii-v / List of Tables --- p.vi / List of Figures --- p.vii / Abstract --- p.1 / Chapter Chapter 1 : --- Introduction / Chapter 1.1 --- An Introduction to Video Compression --- p.3 / Chapter 1.2 --- Overview of Problems --- p.4 / Chapter 1.2.1 --- Analog Video and Digital Problems --- p.4 / Chapter 1.2.2 --- Low Bit Rate Application Problems --- p.4 / Chapter 1.2.3 --- Real Time Video Compression Problems --- p.5 / Chapter 1.2.4 --- Source Coding and Channel Coding Problems --- p.6 / Chapter 1.2.5 --- Bit-rate and Quality Problems --- p.7 / Chapter 1.3 --- Organization of the Thesis --- p.7 / Chapter Chapter 2 : --- Background and Related Work / Chapter 2.1 --- Introduction --- p.9 / Chapter 2.1.1 --- Analog Video --- p.9 / Chapter 2.1.2 --- Digital Video --- p.10 / Chapter 2.1.3 --- Color Theory --- p.10 / Chapter 2.2 --- Video Coding --- p.12 / Chapter 2.2.1 --- Predictive Coding --- p.12 / Chapter 2.2.2 --- Vector Quantization --- p.12 / Chapter 2.2.3 --- Subband Coding --- p.13 / Chapter 2.2.4 --- Transform Coding --- p.14 / Chapter 2.2.5 --- Hybrid Coding --- p.14 / Chapter 2.3 --- Transform Coding --- p.15 / Chapter 2.3.1 --- Discrete Cosine Transform --- p.16 / Chapter 2.3.1.1 --- 1-D Fast Algorithms --- p.16 / Chapter 2.3.1.2 --- 2-D Fast Algorithms --- p.17 / Chapter 2.3.1.3 --- Multidimensional DCT Algorithms --- p.17 / Chapter 2.3.2 --- Quantization --- p.18 / Chapter 2.3.3 --- Entropy Coding --- p.18 / Chapter 2.3.3.1 --- Huffman Coding --- p.19 / Chapter 2.3.3.2 --- Arithmetic Coding --- p.19 / Chapter Chapter 3 : --- Existing Compression Scheme / Chapter 3.1 --- Introduction --- p.20 / Chapter 3.2 --- Motion JPEG --- p.20 / Chapter 3.3 --- MPEG --- p.20 / Chapter 3.4 --- H.261 --- p.22 / Chapter 3.5 --- Other Techniques --- p.23 / Chapter 3.5.1 --- Fractals --- p.23 / Chapter 3.5.2 --- Wavelets --- p.23 / Chapter 3.6 --- Proposed Solution --- p.24 / Chapter 3.7 --- Summary --- p.25 / Chapter Chapter 4 : --- Fast 3D-DCT Algorithms / Chapter 4.1 --- Introduction --- p.27 / Chapter 4.1.1 --- Motivation --- p.27 / Chapter 4.1.2 --- Potentials of 3D DCT --- p.28 / Chapter 4.2 --- Three Dimensional Discrete Cosine Transform (3D-DCT) --- p.29 / Chapter 4.2.1 --- Inverse 3D-DCT --- p.29 / Chapter 4.2.2 --- Forward 3D-DCT --- p.30 / Chapter 4.3 --- 3-D FCT (3-D Fast Cosine Transform Algorithm --- p.30 / Chapter 4.3.1 --- Partitioning and Rearrangement of Data Cube --- p.30 / Chapter 4.3.1.1 --- Spatio-temporal Data Cube --- p.30 / Chapter 4.3.1.2 --- Spatio-temporal Transform Domain Cube --- p.31 / Chapter 4.3.1.3 --- Coefficient Matrices --- p.31 / Chapter 4.3.2 --- 3-D Inverse Fast Cosine Transform (3-D IFCT) --- p.32 / Chapter 4.3.2.1 --- Matrix Representations --- p.32 / Chapter 4.3.2.2 --- Simplification of the calculation steps --- p.33 / Chapter 4.3.3 --- 3-D Forward Fast Cosine Transform (3-D FCT) --- p.35 / Chapter 4.3.3.1 --- Decomposition --- p.35 / Chapter 4.3.3.2 --- Reconstruction --- p.36 / Chapter 4.4 --- The Fast Algorithm --- p.36 / Chapter 4.5 --- Example using 4x4x4 IFCT --- p.38 / Chapter 4.6 --- Complexity Comparison --- p.43 / Chapter 4.6.1 --- Complexity of Multiplications --- p.43 / Chapter 4.6.2 --- Complexity of Additions --- p.43 / Chapter 4.7 --- Implementation Issues --- p.44 / Chapter 4.8 --- Summary --- p.46 / Chapter Chapter 5 : --- Quantization / Chapter 5.1 --- Introduction --- p.49 / Chapter 5.2 --- Dynamic Ranges of 3D-DCT Coefficients --- p.49 / Chapter 5.3 --- Distribution of 3D-DCT AC Coefficients --- p.54 / Chapter 5.4 --- Quantization Volume --- p.55 / Chapter 5.4.1 --- Shifted Complement Hyperboloid --- p.55 / Chapter 5.4.2 --- Quantization Volume --- p.58 / Chapter 5.5 --- Scan Order for Quantized 3D-DCT Coefficients --- p.59 / Chapter 5.6 --- Finding Parameter Values --- p.60 / Chapter 5.7 --- Experimental Results from Using the Proposed Quantization Values --- p.65 / Chapter 5.8 --- Summary --- p.66 / Chapter Chapter 6 : --- Entropy Coding / Chapter 6.1 --- Introduction --- p.69 / Chapter 6.1.1 --- Huffman Coding --- p.69 / Chapter 6.1.2 --- Arithmetic Coding --- p.71 / Chapter 6.2 --- Zero Run-Length Encoding --- p.73 / Chapter 6.2.1 --- Variable Length Coding in JPEG --- p.74 / Chapter 6.2.1.1 --- Coding of the DC Coefficients --- p.74 / Chapter 6.2.1.2 --- Coding of the DC Coefficients --- p.75 / Chapter 6.2.2 --- Run-Level Encoding of the Quantized 3D-DCT Coefficients --- p.76 / Chapter 6.3 --- Frequency Analysis of the Run-Length Patterns --- p.76 / Chapter 6.3.1 --- The Frequency Distributions of the DC Coefficients --- p.77 / Chapter 6.3.2 --- The Frequency Distributions of the DC Coefficients --- p.77 / Chapter 6.4 --- Huffman Table Design --- p.84 / Chapter 6.4.1 --- DC Huffman Table --- p.84 / Chapter 6.4.2 --- AC Huffman Table --- p.85 / Chapter 6.5 --- Implementation Issue --- p.85 / Chapter 6.5.1 --- Get Category --- p.85 / Chapter 6.5.2 --- Huffman Encode --- p.86 / Chapter 6.5.3 --- Huffman Decode --- p.86 / Chapter 6.5.4 --- PutBits --- p.88 / Chapter 6.5.5 --- GetBits --- p.90 / Chapter Chapter 7 : --- "Contributions, Concluding Remarks and Future Work" / Chapter 7.1 --- Contributions --- p.92 / Chapter 7.2 --- Concluding Remarks --- p.93 / Chapter 7.2.1 --- The Advantages of 3D DCT codec --- p.94 / Chapter 7.2.2 --- Experimental Results --- p.95 / Chapter 7.1 --- Future Work --- p.95 / Chapter 7.2.1 --- Integer Discrete Cosine Transform Algorithms --- p.95 / Chapter 7.2.2 --- Adaptive Quantization Volume --- p.96 / Chapter 7.2.3 --- Adaptive Huffman Tables --- p.96 / Appendices: / Appendix A : The detailed steps in the simplification of Equation 4.29 --- p.98 / Appendix B : The program Listing of the Fast DCT Algorithms --- p.101 / Appendix C : Tables to Illustrate the Reording of the Quantized Coefficients --- p.110 / Appendix D : Sample Values of the Quantization Volume --- p.111 / Appendix E : A 16-bit VLC table for AC Run-Level Pairs --- p.113 / References --- p.115

Trois thèmes ont été poursuivis dans la thèse : -On introduit les fonctions symétriques non commutatives dans le cadre des extensions de Ore. On généralise les résultats obtenus par Gelfand, Retakh et Wilson. Notre méthode est en outre plus naturelle et évite l’utilisation des quasi déterminants. -On montre que les factorisations des polynômes de Wedderburn sont en bijection avec des drapeaux complets d’espaces vectoriels provenant de noyaux d’applications polynomiales en des transformations pseudo-linéaires. D’autres résultats, motivés par la théorie des codes, concernent la factorisation dans des anneaux de Ore construits sur des corps finis. On y montre, en particulier, comment se ramener au cas d’un anneau de polynômes classique. -On caractérise l’existence de P.P.C.M. à gauche de polynômes linéaires dans des extensions de Ore sur des anneaux quelconques. Dans ce cadre, une étude détaillée des transformations pseudo-linéaires s’est révélée, une fois encore, un outil indispensable. / Three themes have been pursued in the thesis : We introduce the noncommutative symmetric functions in the frame of Ore extensions. We generalize the results obtained by Gelfand, Retakh and Wilson. Moreover our method is more natural and avoid the use of quasideterminants. We show that the factorizations of Wedderburn polynomials are in bijection with complete flags of vector spaces coming from kernels of polynomial maps in pseudo-linear transformations. Other results, motivated by coding theory, concern the factorizations in Ore extension over finite fields. In particular, we show how to translate factorisations in these rings into factorisations in the usual polynomial rings. We characterize the existence of L.L.C.M of linear polynomials in Ore extensions over general rings. In this frame, a detailed study of pseudo-linear transformations was necessary.

No description available.

Tradicionalmente, os estudos que tinham a exploração pecuária como foco, se limitavam a análise de seus indicadores produtivos e econômicos, ou seja, dava-se um enfoque parcial, setorial ou disciplinar. Igualmente, de um ponto de vista estático e baixo equilíbrio. Por sua vez, a exploração pecuária é um sistema aberto, submetido à influência de um entorno que denominamos ambiente, e que, gerido pelo pecuarista, persegue determinadas finalidades. Por conseqüência, a exploração pecuária é sensível a um amplo leque de fatores de natureza biofísica, sociológica, econômica e de políticas. Neste sentido, as explorações pecuárias como sistemas sociais, são dinâmicas, reativas ou evolutivas, o que significa que as características mais importantes aparecem ao longo do tempo. Por isso, o estudo dos sistemas pecuários requer a consideração explícita da dita variável, tempo. O presente estudo pretende dar resposta a seguinte questão: que mudanças aconteceram nas explorações pecuárias da região de Basalto como reação aos condicionantes do entorno socioeconômico, em constante mudança, mas também, dependentes de fatores e características internas a própria exploração? A região de Basalto, a mais extensa do Uruguai, correspondente a 21% do território nacional, é caracterizada fundamentalmente por estar associada a sistemas extensivos de produção pecuária de baixa produtividade e investimento, onde pastoreiam conjuntamente, bovinos e ovinos. A abordagem metodológica utilizada neste estudo baseou-se na comparação do processamento de informações correspondentes aos anos 1994 e 2008, utilizando como ferramenta, entrevistas dirigidas as mesmas explorações pecuárias da região de Basalto com áreas superiores a 200 hectares. O reconhecimento das mudanças ocorridas nos sistemas pecuários da região de Basalto, no marco das transformações recentes do setor agropecuário do Uruguai, é fundamental para explorar evoluções distintas da pecuária extensiva daquela região, apesar da incerteza a respeito das políticas agrárias dos condicionantes socioeconômicos. Os resultados encontrados sugerem a existência de fatores que ameaçam a continuidade das explorações pecuárias em longo prazo e, conseqüentemente, a sustentabilidade dos ecossistemas pastoris. Estes fatores são de natureza diversa: ambientais econômicos e sociais. / Traditionally, the livestock production studies limited the analysis to productive and economic results, which is to say from a partial approach, or from only one discipline. Also, they were done from a static point of view and supposing a situation at equilibrium. However, the livestock farm is an open system, exposed the influence of its environment, and managed by livestock farmers who have certain purposes. Consequently, the cattle operation is sensible to an ample variety of factors of biophysical, sociological, economic, and ecological nature and also to policies. In this sense, the cattle operations like social systems are dynamic, reactive or adaptive, which means that the most important characteristics appear on the long time. For this reason, the study of the cattle systems requires the explicit consideration this variable, time. The present study tries to give answer to the following question: What changes arose in the cattle operations of the Basalt reacting to the conditions of the socio-economic environment in constant change, but also depending on the own operation internal factors and characteristics? The Region of the Basalt, the most extensive of Uruguay, 21% of the national territory, has been characterized essentially as having extensive systems of cattle production of low productivity and investment; where bovine and ovine graze simultaneously. The methodological approach in this study is based on the comparison of information corresponding to years 1994 and 2008, from the same sample of farms - of the Region of the Basalt with surfaces majors to the 200 hectares -. The data of the changes occurred in the cattle systems of the Basalt Region within the framework of the recent transformations of the farming sector of Uruguay, is fundamental to explore extensive cattle ranch different evolutions, in presence of the uncertainty with respect to the agrarian policies and to the socio-economic conditions. The results suggest the existence of factors that threaten the continuity of the cattle operations in the long term, and therefore, the sustainability of the pastoral ecosystems. These factors are of diverse nature: environmental, economic and social.

Leung, Ching Yee = LMG模型中的保真度對數和絶熱要求 / 梁靜儀. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2010. / Includes bibliographical references (leaves 53-58). / Abstracts in English and Chinese. / Leung, Ching Yee = LMG mo xing zhong de bao zhen du dui shu he jue re yao qiu / Liang Jingyi. / Chapter 1 --- Quantum phase transition and fidelity --- p.1 / Chapter 1.1 --- What is a quantum phase transition --- p.1 / Chapter 1.2 --- Use of fidelity in describing QPT --- p.3 / Chapter 1.3 --- Quantum fidelity versus classical fidelity --- p.5 / Chapter 1.4 --- Motivation of the project --- p.8 / Chapter 2 --- Introduction to LMG model --- p.11 / Chapter 2.1 --- The LMG model --- p.11 / Chapter 2.2 --- General ground-state solution of LMG model --- p.13 / Chapter 2.3 --- Analytical solution of ground-state fidelity of LMG model --- p.16 / Chapter 2.4 --- Numerical diagonalization of the Hamiltonian --- p.23 / Chapter 3 --- Scaling dependence of logarithmic fidelity in the LMG model --- p.26 / Chapter 3.1 --- Symmetry-broken phase --- p.26 / Chapter 3.2 --- Polarized phase --- p.29 / Chapter 3.3 --- Scaling behavior of logarithmic fidelity around the critical point --- p.30 / Chapter 4 --- Quench dynamics --- p.35 / Chapter 4.1 --- Introduction to quench dynamics --- p.35 / Chapter 4.2 --- Quantum adiabatic theorem --- p.35 / Chapter 4.3 --- Ground-state quench dynamics --- p.37 / Chapter 4.4 --- Motivation --- p.38 / Chapter 4.5 --- "Adiabaticity, residue energy and fidelity" --- p.39 / Chapter 4.6 --- Adiabatic requirement --- p.40 / Chapter 5 --- LMG model in quench dynamics --- p.42 / Chapter 5.1 --- Numerical analysis method --- p.42 / Chapter 5.2 --- Loss of adiabaticity --- p.44 / Chapter 5.3 --- The adiabatic requirement in the symmetry-broken phase --- p.45 / Chapter 5.4 --- The adiabatic requirement in the polarized phase --- p.46 / Chapter 5.5 --- In the critical region --- p.47 / Chapter 6 --- Summary --- p.50 / Chapter 6.1 --- Scaling dependence of logarithmic fidelity --- p.50 / Chapter 6.2 --- Scaling dependence of duration time in quench dynamics --- p.52 / Bibliography --- p.53

Kwok, Ho Man = 多體系統中的量子臨界現象與保真度 / 郭灝民. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2008. / Includes bibliographical references (p. 106-109). / Abstracts in English and Chinese. / Kwok, Ho Man = Duo ti xi tong zhong de liang zi lin jie xian xiang yu bao zhen du / Guo Haomin. / Chapter 1 --- Overview of Quantum Phase transitions --- p.1 / Chapter 1.1 --- Classification of QPTs --- p.2 / Chapter 1.2 --- Teaching model: The quantum Ising model --- p.4 / Chapter 1.3 --- Critical exponents and universality classes --- p.6 / Chapter 1.4 --- A new tool to the QPT: Fidelity --- p.8 / Chapter 1.5 --- Fidelity susceptibility --- p.12 / Chapter 1.6 --- Motivation of this report --- p.16 / Chapter 2 --- Analysis of the One Dimensional Quantum XY model --- p.17 / Chapter 2.1 --- Introduction to the model Hamiltonian --- p.17 / Chapter 2.2 --- Diagonalizing the Hamiltonian --- p.18 / Chapter 2.2.1 --- Jordan-Wigner transformation --- p.18 / Chapter 2.2.2 --- Bogoliubov transformation --- p.22 / Chapter 2.3 --- Ground state properties --- p.24 / Chapter 2.4 --- Calculating the fidelity susceptibility --- p.25 / Chapter 2.5 --- Fidelity susceptibility in Quantum Ising model --- p.31 / Chapter 2.6 --- Numerical comparison --- p.36 / Chapter 3 --- The Lipkin-Meshkov-Glick model --- p.40 / Chapter 3.1 --- Literature Review --- p.40 / Chapter 3.1.1 --- Scaling Behaviour --- p.41 / Chapter 3.1.2 --- Quantum Phase Transition --- p.42 / Chapter 3.1.3 --- Mathematical formalism --- p.44 / Chapter 3.1.4 --- Conserved quantities --- p.46 / Chapter 3.2 --- Energy spectrum for isotropic case --- p.47 / Chapter 3.3 --- Energy spectrum for anisotropic case --- p.49 / Chapter 3.3.1 --- The Holstein-Primakoff mapping --- p.49 / Chapter 3.3.2 --- Bogoliubov transformation for Boson systems --- p.53 / Chapter 3.4 --- Fidelity susceptibility in the isotropic case --- p.55 / Chapter 3.4.1 --- h> h0 --- p.56 / Chapter 3.4.2 --- h0 > h> h1 --- p.57 / Chapter 3.4.3 --- h1 > h > h2 --- p.57 / Chapter 3.5 --- Fidelity susceptibility in the anisotropic case --- p.60 / Chapter 3.5.1 --- "h > 1, driving by γ - xF(γ)" --- p.60 / Chapter 3.5.2 --- "h > 1, driving by h - xF(h)" --- p.62 / Chapter 3.5.3 --- "h < 1, driving by γ - xF(γ)" --- p.63 / Chapter 3.5.4 --- "h < 1, driving by h - xF(h)" --- p.64 / Chapter 3.6 --- Discussion and numerical analysis --- p.65 / Chapter 3.7 --- A possible resolution to the isotropic case: Partial-state fidelity and its susceptibility --- p.71 / Chapter 3.7.1 --- Review of the formalism --- p.72 / Chapter 3.7.2 --- Continuous level crossing and fidelity in the isotropic model --- p.74 / Chapter 3.7.3 --- Partial-state fidelity susceptibility --- p.77 / Chapter 4 --- Numerical Approach to Fidelity Susceptibility --- p.81 / Chapter 4.1 --- The Scaling Ansatz and Critical exponents --- p.81 / Chapter 4.2 --- Examples --- p.83 / Chapter 4.2.1 --- One Dimensional Quantum Ising model --- p.83 / Chapter 4.2.2 --- LMG model --- p.86 / Chapter 4.2.3 --- Two Dimensional Quantum Ising model --- p.90 / Chapter 4.2.4 --- Two Dimensional XXZ model --- p.93 / Chapter 4.2.5 --- One Dimensional Heisenberg model --- p.96 / Chapter 4.3 --- Discussion --- p.100 / Chapter 5 --- Summary --- p.105 / Bibliography --- p.106

Chan, Wenling = 某些一維強關聯系統中量子糾纏的行為 / 陳文嶺. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2008. / Includes bibliographical references (leaves 91-97). / Abstracts in English and Chinese. / Chan, Wenling = Mou xie yi wei qiang guan lian xi tong zhong liang zi jiu chan de xing wei / Chen Wenling. / Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- Entanglement --- p.1 / Chapter 1.2 --- Thermal entanglement --- p.4 / Chapter 1.3 --- Quantum information theory and correlations --- p.5 / Chapter 1.4 --- Quantum phase transition --- p.9 / Chapter 1.5 --- Motivation of our study --- p.12 / Chapter 2 --- Entanglement measures --- p.14 / Chapter 2.1 --- Criteria for a good entanglement measure --- p.14 / Chapter 2.2 --- Some popular entanglement measures --- p.17 / Chapter 2.2.1 --- Entropy of entanglement --- p.17 / Chapter 2.2.2 --- Entanglement of formation --- p.18 / Chapter 2.2.3 --- Concurrence --- p.20 / Chapter 2.2.4 --- Negativity --- p.21 / Chapter 2.2.5 --- Other measures --- p.22 / Chapter 3 --- Maximizing thermal entanglement using magnetic fields --- p.24 / Chapter 3.1 --- XY model --- p.24 / Chapter 3.2 --- Measurement of thermal entanglement --- p.26 / Chapter 3.3 --- Configurations of fields for maximal thermal entanglement --- p.27 / Chapter 4 --- Correlations in quantum systems --- p.36 / Chapter 4.1 --- Definitions and measures of bipartite correlations --- p.37 / Chapter 4.1.1 --- Total correlation --- p.37 / Chapter 4.1.2 --- Quantum correlation --- p.38 / Chapter 4.1.3 --- Classical correlation --- p.39 / Chapter 4.2 --- Environmental effects on correlations --- p.42 / Chapter 4.2.1 --- Anisotropic Heisenberg model --- p.42 / Chapter 4.2.2 --- XY model with nonuniform magnetic field --- p.44 / Chapter 5 --- Quantum phase transition in asymmetric Hubbard model --- p.51 / Chapter 5.1 --- Asymmetric Hubbard model --- p.51 / Chapter 5.1.1 --- The Hamiltonian --- p.52 / Chapter 5.1.2 --- Perturbation expansion in large-U limit --- p.53 / Chapter 5.1.3 --- The phases --- p.54 / Chapter 5.2 --- Density-matrix renormalization group (DMRG) method --- p.57 / Chapter 5.2.1 --- Basic concepts --- p.58 / Chapter 5.2.2 --- Algorithm --- p.60 / Chapter 5.2.3 --- Measurements of observables --- p.67 / Chapter 5.2.4 --- Improvements --- p.68 / Chapter 5.3 --- Entanglement as the phase transition indicator --- p.71 / Chapter 5.3.1 --- Two-site entanglement --- p.72 / Chapter 5.3.2 --- Block entanglement --- p.73 / Chapter 5.4 --- Numerical results and analysis --- p.74 / Chapter 5.4.1 --- Away from half-filling --- p.74 / Chapter 5.4.2 --- Half-filling --- p.79 / Chapter 6 --- Conclusion --- p.88 / Bibliography --- p.91

Li, Ying Wai = 安德森模型下量子相變的數值研究 / 李盈慧. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2007. / Includes bibliographical references (leaves 69-72). / Text in English; abstracts in English and Chinese. / Li, Ying Wai = Andesen mo xing xia liang zi xiang bian de shu zhi yan jiu / Li, Yinghui. / Chapter 1 --- Review on Anderson Models and Quantum Phase Transitions --- p.1 / Chapter 1.1 --- The Anderson Impurity Model --- p.1 / Chapter 1.2 --- The Periodic Anderson Model --- p.2 / Chapter 1.3 --- Quantum Phase Transitions (QPTs) --- p.3 / Chapter 1.4 --- Motivation of this project --- p.4 / Chapter 2 --- Studies on the Ground State Energy of Periodic Anderson Model --- p.7 / Chapter 2.1 --- Background --- p.7 / Chapter 2.2 --- Hamiltonian and Physical Meanings of Lattice Anderson Model --- p.8 / Chapter 2.2.1 --- The first term: -t ´iσ （c+̐ưσci+lσ + h.c.) --- p.8 / Chapter 2.2.2 --- The second term: Ef´iσ̐ưfiσ --- p.9 / Chapter 2.2.3 --- The third term: V ´ ̐ưσ (c+iσ̐ư̐ưσ + h.c.) --- p.9 / Chapter 2.2.4 --- The fourth term: U ̐ưσ´ nfitnfi↓ --- p.9 / Chapter 2.2.5 --- The whole Hamiltonian --- p.10 / Chapter 2.3 --- Non-Interacting Case of Lattice Anderson Model --- p.10 / Chapter 2.3.1 --- The Hamiltonian in momentum space --- p.11 / Chapter 2.3.2 --- The conduction band eK --- p.12 / Chapter 2.3.3 --- The band energies ±K --- p.12 / Chapter 2.3.4 --- The energy band gap Δ --- p.14 / Chapter 2.3.5 --- Green's functions at finite temperature --- p.14 / Chapter 2.4 --- Perturbation in U for symmetric model --- p.16 / Chapter 2.4.1 --- Previous Results --- p.16 / Chapter 2.4.2 --- Ground state energy at finite temperature by time-dependent perturbation theory --- p.18 / Chapter 3 --- Numerical Integration using Wang-Landau Sampling --- p.22 / Chapter 3.1 --- Background --- p.22 / Chapter 3.2 --- Wang-Landau integration --- p.25 / Chapter 3.2.1 --- Description of the method --- p.25 / Chapter 3.2.2 --- Correspondence between Wang-Landau sampling for physical systems and Wang-Landau integration --- p.27 / Chapter 3.3 --- Results --- p.28 / Chapter 3.3.1 --- Application to one- and two-dimensional test integrals . --- p.28 / Chapter 3.3.2 --- An example of a potential application: Perturbative calculation of the lattice Anderson model --- p.31 / Chapter 3.3.3 --- Discussion and summary --- p.35 / Chapter 4 --- Studies on QPT of Anderson Impurity Model by Quantum Entanglement --- p.38 / Chapter 4.1 --- Background --- p.38 / Chapter 4.2 --- Formalism --- p.39 / Chapter 4.2.1 --- Hamiltonian --- p.39 / Chapter 4.2.2 --- Conditions Used in Our Study --- p.40 / Chapter 4.2.3 --- Quantifying Quantum Entanglement: Entropy and Concurrence --- p.41 / Chapter 4.3 --- Numerical Results --- p.45 / Chapter 4.3.1 --- Method --- p.45 / Chapter 4.3.2 --- Finite Size Effects of the Ground State Energy --- p.46 / Chapter 4.3.3 --- Finite Size Effects of the Von Neumann Entropy --- p.49 / Chapter 4.3.4 --- Finite Size Effects of the Fermionic Concurrence --- p.53 / Chapter 4.4 --- Summary --- p.58 / Chapter 5 --- Fidelity in Critical Phenomena --- p.59 / Chapter 5.1 --- Background --- p.59 / Chapter 5.2 --- Ground State Fidelity and Dynamic Structure Factor --- p.60 / Chapter 5.3 --- Mixed-state fidelity and thermal phase transitions --- p.63 / Chapter 5.4 --- Summary --- p.64 / Chapter 6 --- Conclusion --- p.66 / Bibliography --- p.69

No description available.