Typescript (photocopy). / Digitized by Kansas Correctional Industries

Thesis. 1977. Ph.D.--Massachusetts Institute of Technology. Dept. of Physics. / M̲i̲c̲ṟo̲f̲i̲c̲ẖe̲ c̲o̲p̲y̲ a̲v̲a̲i̲ḻa̲ḇḻe̲ i̲ṉ A̲ṟc̲ẖi̲v̲e̲s̲ a̲ṉḏ S̲c̲i̲e̲ṉc̲e̲. / Vita. / Bibliography : leaf 134. / Ph.D.

Thesis. 1976. M.S.--Massachusetts Institute of Technology. Dept. of Electrical Engineering and Computer Science. / Microfiche copy available in Archives and Engineering. / Includes bibliographical references. / M.S.

Thesis. 1978. Sc.D.--Massachusetts Institute of Technology. Dept. of Materials Science and Engineering. / MICROFICHE COPY AVAILABLE IN ARCHIVES AND SCIENCE. / Vita. / Includes bibliographical references. / Sc.D.

Thesis (Sc.D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 1981. / MICROFICHE COPY AVAILABLE IN ARCHIVES AND ENGINEERING. / Vita. / Bibliography: leaves 146-150. / by Monson H. Hayes III. / Sc.D.

This PhD thesis consists of five complementary chapters. Chapters 2 through 4 constitute the basis of research papers to be published subsequently. These three chapters summarize the state of a single crystal undergoing elastoplastic deformation. The studies presented in this thesis primarily deal with experimental and computational concepts that enable the calculation, measurement and extraction of the spatially resolved net Burgers density vector and the geometrically necessary dislocation densities (GNDs), which reveal the small scale continuum characteristics of a single crystal in the elastoplastic state. The calculation methodology of a new validation parameter, β, which is the orientation of the net Burgers density vector, is given in chapter 2. This new parameter, β, enables us to validate the elastic-plastic constitutive relations. Since the existing methods used for validation cannot give direct information about the state of the material, the β-variable is introduced for elastic- plastic constitutive models. β-fields, which are essentially contour maps of β-variables on two dimensional spatial coordinates, are used to monitor the activity regions of effective slip systems. Chapters 2 through 4 present a comprehensive analysis of the spatially resolved net Burgers density vector, along with the length scale characterization of dislocation structures and validation of constitutive relations. The studies presented in this work are the outcome of experimental and computational research. The experimental work consists of the indentation of a nickel single crystal deformed through a quasi-statically applied line load parallel to the [110] crystallographic orientation. The line load was applied onto (001) surface of the single crystal by a tungsten carbide wedge indenter with a 90◦ included angle. A two-dimensional deformation field on an indented single crystal, in which the only non-zero lattice rotation occurs in the plane of deformation and only three effective in-plane slip systems are activated, was investigated. The mid-section of the deformed single crystal was exposed by EDM and polished electrochemically. The in-plane lattice rotations were measured by high-resolution electron backscattered diffraction (HR-EBSD). The Nye's dislocation density components, lattice curvatures, GNDs and net Burgers density vectors were calculated. Therefore, the β- variable and the β-fields are calculated both experimentally, analytically and numerically in Chapter 2. A qualitative comparison of the three methods showed that the β-field obtained from experimental measurements agrees with those obtained from analytical and numerical methods. The directions of the net Burgers density vector, which are used to determine the boundaries of the slip activity regions, are also given in Chapter 2. Chapter 3 mainly deals with the hardening parameters associated with strain hardening rules utilized in finite element simulations, and investigates the sensitivity of the β-variable to parameters such as latent hardening ratio, initial hardening modulus and saturation strength. The study revealed that a change in the saturation strength has a significant effect on both magnitude of the β-variable and the boundary of the slip activity regions. Chapter 4 presents a length scale analysis associated with dislocation structures such as cell size and cell wall width. The methods presented in this chapter employ the SEM- based continuum method and Fourier Analysis. As-measured GNDs are extracted along the local crystallographic traces, and a quasi-periodic arrangement of dislocation structures is obtained. The extracted GND functions are truncated, interpolated, and filtered. Finally, Fourier Transform is applied to obtain a relationship between cell size and cell wall width of the dislocation structures. The results are compared with those obtained by TEM micrographs. Whereas TEM micrographs characterize the dislocation structures in small scale, the method that is presented in this chapter provides multi scale characterization, which is an order of magnitude larger. Concluding remarks and recommendations for future studies are given in Chapter 5.

Este trabalho discute a permanência dos espaços públicos centrais frente às sucessivas transformações metropolitanas e seu papel na construção da cidade. A partir de uma praça signifi cativa da ocupação territorial de São Paulo, a Praça do Patriarca, procuramos apontar, no espaço construído, as imposições e as possibilidades defi nidas ao longo do processo histórico e dos diversos ideais urbanos responsáveis pela sua confi- guração. A Praça e seu entorno foram observados quanto à conformação espacial, ao desenho formal de seus edifícios e às possibilidades de uso e apropriação que permitia em cada período estudado. A esse levantamento, foram sobrepostas referências históricas sobre a construção da cidade e seus distintos propósitos, procurando esclarecer as relações entre a conjuntura sócio-política e a consequente construção do espaço. / This work discusses the permanence of central public spaces in between the successive urban transformations and their role in the construction of the city. As off the Praça do Patriarca, an important square for the territorial occupation of São Paulo, we will show the impositions and possibilities defi ned during historic process in the constructed space and the various urban concepts responsible for its confi guration. The relation of the square and its environment was researched concerning their spatial confi guration, the formal design of their buildings and the possibilities of use and appropriation permitted during each of the observed periods. Added to this survey were historic references about the city construction and their distinct purposes, with the idea to show the relationship between a current social-politic situation and the resulting spatial construction.

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

Yu, Wing Chi = 多體系統中的量子相變動力學 / 余詠芝. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2011. / Includes bibliographical references (leaves 94-99). / Abstracts in English and Chinese. / Yu, Wing Chi = Duo ti xi tong zhong de liang zi xiang bian dong li xue / Yu Yongzhi. / Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- Quantum phase transitions --- p.1 / Chapter 1.2 --- Schemes detecting QPTs --- p.3 / Chapter 1.2.1 --- Traditional schemes --- p.3 / Chapter 1.2.2 --- Quantum Entanglement --- p.4 / Chapter 1.2.3 --- Quantum fidelity --- p.4 / Chapter 1.2.4 --- Loschmidt echoes --- p.5 / Chapter 1.2.5 --- Quench dynamics --- p.6 / Chapter 1.3 --- Motivation --- p.7 / Chapter 2 --- Theoretical framework --- p.9 / Chapter 2.1 --- Quantum Zeno effect --- p.9 / Chapter 2.2 --- Mathematical formulation --- p.11 / Chapter 2.3 --- Remarks --- p.14 / Chapter 3 --- Analysis on the One-dimensional Transverse-field Ising model --- p.17 / Chapter 3.1 --- The model --- p.17 / Chapter 3.2 --- Diagonalization of the Hamiltonian --- p.20 / Chapter 3.2.1 --- Jordan-Wigner transformation --- p.20 / Chapter 3.2.2 --- Fourier Transformation --- p.24 / Chapter 3.2.3 --- Bogoliubov transformation --- p.26 / Chapter 3.3 --- Quantum Zeno dynamics in the model --- p.28 / Chapter 3.3.1 --- Analytical calculation of the Zeno susceptibility --- p.28 / Chapter 3.3.2 --- Validity of the analytical result --- p.31 / Chapter 3.3.3 --- Scaling behavior of the Zeno susceptibility --- p.33 / Chapter 3.3.4 --- Zeno susceptibility around the critical point --- p.35 / Chapter 3.4 --- Conclusion and experimental outlook --- p.38 / Chapter 4 --- Analysis on the Lipkin-Meshkov-Glick Model --- p.40 / Chapter 4.1 --- The model --- p.41 / Chapter 4.2 --- Diagonalization of the Hamiltonian --- p.46 / Chapter 4.2.1 --- Holstein-Primakoff transformation --- p.46 / Chapter 4.2.2 --- Bogoliubov transformation --- p.49 / Chapter 4.3 --- Quantum Zeno dynamics in the model --- p.51 / Chapter 4.3.1 --- Analytical form of the Zeno susceptibility and its scaling behavior --- p.51 / Chapter 4.3.2 --- Validity of the analytical result --- p.54 / Chapter 4.3.3 --- Numerical analysis of the Zeno susceptibility --- p.55 / Chapter 4.4 --- Conclusion --- p.60 / Chapter 5 --- Analysis on the Kitaev model on a honeycomb lattice --- p.61 / Chapter 5.1 --- The model --- p.61 / Chapter 5.2 --- Diagonalization of the Hamiltonian --- p.63 / Chapter 5.2.1 --- Jordan-Wigner transformation for two-dimensional systems --- p.64 / Chapter 5.2.2 --- Majorana fermion representation --- p.68 / Chapter 5.2.3 --- Fermions on the 之-bonds --- p.71 / Chapter 5.2.4 --- Bogoliubov transformation --- p.73 / Chapter 5.3 --- Energy spectrum --- p.75 / Chapter 5.4 --- Quantum Zeno dynamics in the model --- p.77 / Chapter 5.4.1 --- Coupling along the Jx = Jy line --- p.77 / Chapter 5.4.2 --- Coupling along the line with constant Jz --- p.83 / Chapter 5.5 --- Conclusion --- p.90 / Chapter 6 --- Conclusion and outlook --- p.91 / Bibliography --- p.94 / Chapter A --- Perturbative form of the Loschimdt Echo --- p.100 / Chapter B --- Hellmann-Feynman theorem --- p.107 / Chapter C --- Commutation relations in the Jordan-Wigner transformation --- p.108

In chapter 1, we give an introduction to QPT, and take one-dimensional XXZ model as an example to illustrate the QPT therein. Through this simple example, we would show that when the tunable parameter is varied, the system evolves into different phases, across two quantum QPT points. The distinct phases exhibit very different behaviors. Also a schematic phase diagram is appended. / In chapter 2, we are engaged in research on ordered phases. Originating in the work of Landau and Ginzburg on second-order phase transition, the spontaneous symmetry breaking induces nonzero expectation of field operator, e.g., magnetization M in the Ising model, and then we say long range order (LRO) exists in the system. LRO plays a key role in determining the ordered-disorder transition. Thereby, we investigate two-dimensional 120° orbital-only model to present how to extract the information of LRO in a pedagogical manner, by applying the reflection positivity method introduced by Dyson, Lieb, and Simon. We rigorously establish the existence of an anti-ferromagnetic like transverse orbital long-range order in the so called two-dimensional 120° model at zero temperature. Next we consider possible pairings in the family of FeAs-based ReO1--xFxFeAs (Re=La, Nd, Ce, Pr, etc.) high-temperature superconductors. We build some identities based on a two-orbital model, and obtained some constraints on a few possible pairings. We also establish the sufficient conditions for the coexistence of two superconducting orders, and we propose the most favorable pairings around half filling according to physical consideration. / In chapter 3, we present a quantum solvation process with solvent of fermion character based on the one-dimensional asymmetric t-J-Jz model. The model is experimental realizable in optical lattices and exhibits rich physics. In this work, we show that there exist two types of phase separations, one is driven by potential energy while the other by kinetic energy. In between, solvation process occurs. Analytically, we are able to obtain some rigorous results to understand the underlying physics. Numerically, we perform exact diagonalization and density matrix renormalization group calculations, accompanied by detailed finite size analysis. / In chapter 4, we explore several characterizations of QPT points. As distinguished from the methods in condensed-matter physics, we give much attention to understand QPT from the quantum information (QI) point of view. The perspective makes a new bridge between these two fields. It no only can facilitate the understanding of condensed-matter physics, but also provide the prominent playground for the quantum information theory. They are fidelity susceptibility and reduced fidelity susceptibility. We establish a general relation between fidelity and structure factor of the driving term in a Hamiltonian through fidelity susceptibility and show that the evaluation of fidelity in terms of susceptibility is facilitated by using well developed techniques such as density matrix renormalization group for the ground state, or Monte Carlo simulations for the states in thermal equilibrium. Furthermore, we show that the reduced fidelity susceptibility in the family of one-dimensional XY model obeys scaling law in the vicinity of quantum critical points both analytically and numerically. The logarithmic divergence behavior suggests that the reduced fidelity susceptibility can act as an indicator of quantum phase transition. / Quantum Phase Transition (QPT) describes the non-analytic behaviors of the ground-state properties in a many-body system by varying a physical parameter at absolute zero temperature - such as magnetic field or pressure, driven by quantum fluctuations. Such quantum phase transitions can be first-order phase transition or continuous. The phase transition is usually accompanied by a qualitative change in the nature of the correlations in the ground state, and describing this change shall clearly be one of our major interests. We address this issue from three prospects in a few strong correlated many-body systems in this thesis, i.e., identifying the ordered phases, studying the properties of different phases, characterizing the QPT points. / The past decade has seen a substantial rejuvenation of interest in the study of quantum phase transitions (QPTs), driven by experimental advance on the cuprate superconductors, the heavy fermion materials, organic conductors, Quantum Hall effect, Fe-As based superconductors and other related compounds. It is clear that strong electronic interactions play a crucial role in the systems of current interest, and simple paradigms for the behavior of such systems near quantum critical points remain unclear. Furthermore, the rapid progress in Feshbach resonance and optical lattice provides a flexible platform to study QPT. / You, Wenlong = 強關聯多體體系中的量子相變 / 尤文龍. / Adviser: Hai Qing Lin. / Source: Dissertation Abstracts International, Volume: 70-09, Section: B, page: . / Thesis (Ph.D.)--Chinese University of Hong Kong, 2009. / Includes bibliographical references (leaves 104-115). / 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, [200-] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Abstracts in English and Chinese. / School code: 1307. / You, Wenlong = Qiang guan lian duo ti ti xi zhong de liang zi xiang bian / You Wenlong.