Ultracold molecules promise a revolutionary test bed for quantum science with applications ranging from experiments that probe the nature of our universe, to hosting new platforms for quantum computing. Cooling and trapping molecules in the ultracold regime is the first step to unlocking the wide array of proposed applications, and developing these techniques to control molecules is a key but challenging research field. In this thesis, we describe progress towards a new apparatus designed to cool and trap barium monohydride (BaH), a molecule that is amenable to laser cooling and has prospects as a precursor for ultracold atomic hydrogen. The same complexity that makes molecules interesting objects of study creates challenges for optical control. To mitigate some of these challenges, we first cool the molecules using cryogenic techniques and technologies. Our apparatus uses a cryogenic buffer gas to thermalize BaH within a contained cell. The molecules are extracted into a beam with millikelvin transverse temperature, and forward velocities <100 m/s. The BaH beam in this work is the brightest hydride beam to date, with molecule density and kinetic characteristics well suited for laser cooling and trapping.

The need for efficient, cheap, and durable semiconductors for photovoltaic and optoelectronic applications has spurred a number of dramatic recent developments in semiconductor quantum physics. Aided by advanced synthetic and characterization techniques, the development of high-quality, nano-structured, tunable materials has resulted in the observation of many novel phenomena. The goal of this thesis is to develop and apply methods in theoretical condensed matter science to the study of these promising materials. In Chapter 1 I explore methylammonium lead iodide (MAPbI3), a paradigmatic hybrid organic-inorganic perovskite system. To explain charge carrier dynamics in this material, I develop a microscopic tight-binding model. The average band structure is calculated and the magnitude of the temperature-dependent band gap opening and Urbach energy is quantified. The charge carrier mobility is calculated within a linear response formalism and its temperature dependence is characterized. Overall, the fully ab initio model is found to explain several non-trivial experimental phenomena while making minimal assumptions concerning the nature of the electron-phonon coupling and the character of the nuclear motion in these materials. In Chapters 2 and 3, I turn to the subject of atomically-thin transition metal dichalcogenides. I improve upon past variational calculations of exciton and trion binding energies in these materials by applying diffusion Monte Carlo to exactly calculate exciton, trion, and biexciton binding energies within an effective few-body Hamiltonian. Carriers are assumed to experience two-body interactions of the Keldysh type that have been parameterized previously from electronic structure calculations. The structures of the exact ground state wavefunctions are calculated and compared to those of the previous variational trial wavefunctions. Next, I calculate the doping dependence of the rate of exciton and trion elastic scattering with free electrons within first-order time-dependent perturbation theory. The calculation provides the first theoretical estimate of the intrinsic trion linewidth in these materials. Finally, in Chapter 4, I study variants of the GW approximation to the one-particle Green's function for calculating correlation energies and spectral weights for the three-dimensional homogeneous electron gas. By relating the cumulant generating function to the improper GW self-energy, I develop a new cumulant-based GW approximation. The approach is compared to existing methods first via solution of a simple linearly-coupled electron phonon model and later through application to the electron gas problem.

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

Chan Yuk-Lin = 並行機上量子自旋模型的對角化 / 陳玉蓮. / Thesis submitted in: September 2004. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2005. / Includes bibliographical references (leaves 121-123). / Text in English; abstracts in English and Chinese. / Chan Yuk-Lin = Bing xing ji shang liang zi zi xuan mo xing de dui jiao hua / Chen Yulian. / Abstract --- p.i / 摘要 --- p.ii / Acknowledgement --- p.iii / Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- Motivation --- p.1 / Chapter 1.2 --- Development of Theory of Magnetism --- p.2 / Chapter 1.3 --- Heisenberg Model --- p.5 / Chapter 1.4 --- Thesis Organization --- p.9 / Chapter 2 --- Introduction to Parallel Computing --- p.11 / Chapter 2.1 --- Architecture of Parallel Computer --- p.12 / Chapter 2.2 --- Symmetric Multiprocessors and Clusters --- p.16 / Chapter 2.2.1 --- Symmetric Multiprocessors --- p.16 / Chapter 2.2.2 --- Cluster --- p.18 / Chapter 2.2.3 --- Clusters versus SMP --- p.19 / Chapter 2.3 --- Hybrid Architectures (Cluster of SMPs) --- p.20 / Chapter 2.4 --- Hardware Platform for Parallel Computing --- p.21 / Chapter 2.4.1 --- SGI Origin 2000 (Origin) --- p.21 / Chapter 2.4.2 --- IBM RS/6000 SP (Orbit) --- p.22 / Chapter 3 --- Parallelization --- p.23 / Chapter 3.1 --- Models of Parallel Programming --- p.24 / Chapter 3.2 --- Parallel Programming Paradigm --- p.26 / Chapter 3.2.1 --- Programming for Distributed Memory Systems: MPI --- p.26 / Chapter 3.2.2 --- Programming for Shared Memory Systems: OpenMP --- p.31 / Chapter 3.2.3 --- Programming for Hybrid Systems: MPI + OpenMP --- p.39 / Chapter 4 --- Performance --- p.42 / Chapter 4.1 --- Writing a Parallel Program --- p.42 / Chapter 4.2 --- Performance Analysis --- p.43 / Chapter 4.3 --- Synchronization and Communication --- p.47 / Chapter 4.3.1 --- Communication modes --- p.47 / Chapter 5 --- Exact Diagonalization --- p.50 / Chapter 5.1 --- Symmetry Invariance --- p.52 / Chapter 5.2 --- Lanczos Method --- p.53 / Chapter 5.2.1 --- Basic Lanczos Algorithm --- p.54 / Chapter 5.2.2 --- Modified Lanczos Method --- p.56 / Chapter 5.3 --- Dynamic Memory Allocation --- p.58 / Chapter 6 --- Parallelization of Exact Diagonalization --- p.62 / Chapter 6.1 --- Parallelization of Lanczos Method --- p.62 / Chapter 6.2 --- Hamiltonian Matrix Decomposition --- p.66 / Chapter 6.2.1 --- Row-Wise Block Decomposition --- p.67 / Chapter 6.2.2 --- Column-Wise Block Decomposition --- p.69 / Chapter 7 --- Results and Discussion --- p.71 / Chapter 7.1 --- Lattice structure --- p.71 / Chapter 7.2 --- Definition of Timing --- p.72 / Chapter 7.3 --- Rowwise vs Columnwise --- p.73 / Chapter 7.4 --- SGI Origin 2000(0rigin) --- p.77 / Chapter 7.4.1 --- Timing Results --- p.77 / Chapter 7.4.2 --- Performance --- p.79 / Chapter 7.5 --- IBM RS/6000 SP(Orbit) --- p.82 / Chapter 7.5.1 --- MPI vs Hybrid --- p.82 / Chapter 7.5.2 --- Timing and Performance --- p.84 / Chapter 7.6 --- Timing on Origin vs Orbit --- p.89 / Chapter 8 --- Conclusion --- p.91 / Chapter A --- Basic MPI Concepts --- p.95 / Chapter A.1 --- Message Passing Interface --- p.95 / Chapter A.2 --- MPI Routine Format --- p.96 / Chapter A.3 --- Start writing a MPI program --- p.96 / Chapter A.3.1 --- The First MPI Program --- p.97 / Chapter A.3.2 --- Sample MPI Program #1 --- p.100 / Chapter A.3.3 --- Sample MPI Program #2 --- p.106 / Chapter B --- Compiling and Running Parallel Jobs in IBM SP --- p.111 / Chapter B.1 --- Compilation --- p.111 / Chapter B.1.1 --- Compiler Options --- p.112 / Chapter B.2 --- Running Jobs --- p.114 / Chapter B.2.1 --- Loadleveler --- p.114 / Chapter B.2.2 --- Serial Job Script --- p.114 / Chapter B.2.3 --- Parallel Job Script : MPI Program --- p.115 / Chapter B.2.4 --- Parallel Job Script: OpenMP Program --- p.117 / Chapter B.2.5 --- Parallel Job Script: Hybrid MPI/OpenMP Program . . --- p.118 / Chapter B.2.6 --- LoadLeveler Commands --- p.120 / Bibliography --- p.123

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&deg; 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&deg; 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.

The research contained within this thesis concerns the detection, identification and effect of charge noise on quantum dot systems. In the first research chapter we study the cross correlation between pairs of exciton qubits subject to a common fluctuating charge environment, whose dynamics are solved using a transfer matrix approach. Our results show that we are able to discern features showing whether or not the charges interact with both quantum dots simultaneously i.e., form a correlated noise source. We find that qubits in a common charge environment display photon bunching, if both dots are driven on resonance or if the laser detunings are equal in both qubits and anitibunching if the laser detunings are in opposite directions. In the second research chapter we study the auto-correlation function of a single optically driven exciton qubit interacting with an environment consisting of 1/f noise and a fluctuating charge. We again use the transfer matrix method and a sum of Lorentzian distributions to approximate 1/f noise. Our simulations show that signatures of 1/f noise do exist in photon correlation measurements. From such measurements we are also able to determine a minimum cut-off frequency of the 1/f noise, in the case that there is such a cut-off. In addition we also show that a 1/f and a single fluctuator can be distinguished using the auto-correlation. In the final research chapter we study a pair of quantum dots, each with a low lying electron spin qubit and one higher lying level that can be selectively optically excited from one of the two spin states. Entanglement between the two spins can be achieved through path erasure. We look at the effect of a single fluctuating charge of the entanglement between these two `L' shaped electronic structures.

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

Fung, Shu Hong = 量子點內自旋弱量度的散粒噪聲相關理論 / 馮書航. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2008. / Includes bibliographical references (p. 80-85). / Abstracts in English and Chinese. / Fung, Shu Hong = Liang zi dian nei zi xuan ruo liang du de san li zao sheng xiang guan li lun / Feng Shuhang. / Chapter 1 --- Introduction --- p.1 / Chapter 2 --- Review on measurement theory --- p.5 / Chapter 2.1 --- Weak measurement --- p.5 / Chapter 2.2 --- POVM formalism --- p.7 / Chapter 2.3 --- Noise spectroscopy --- p.8 / Chapter 3 --- Review on spin decoherence --- p.11 / Chapter 3.1 --- Longitudinal relaxation --- p.12 / Chapter 3.2 --- Transverse relaxation --- p.12 / Chapter 3.3 --- Inhomogeneous broadening --- p.13 / Chapter 3.4 --- Typical relaxation timescales --- p.14 / Chapter 4 --- Proof-of-principle setup --- p.15 / Chapter 4.1 --- Faraday rotation --- p.15 / Chapter 4.2 --- Polarization beam splitter --- p.17 / Chapter 4.3 --- Quantum state of the system --- p.19 / Chapter 5 --- Weak measurement on the spin --- p.22 / Chapter 5.1 --- POVM of measurement --- p.22 / Chapter 5.2 --- POVM of dephasing --- p.25 / Chapter 5.3 --- Interval distribution operator --- p.26 / Chapter 5.4 --- Interval distribution function without dephasing --- p.27 / Chapter 5.5 --- Second order correlation function without dephasing --- p.31 / Chapter 5.6 --- Interval distribution function with dephasing --- p.34 / Chapter 5.7 --- Second order correlation function with dephasing --- p.40 / Chapter 5.8 --- Effect of inhomogeneous broadening on g(2)(t) --- p.42 / Chapter 5.9 --- Third order correlation function --- p.43 / Chapter 5.10 --- Monte Carlo simulation --- p.44 / Chapter 5.11 --- Results and discussion --- p.46 / Chapter 5.11.1 --- Characteristics and implications of g(2)(t) --- p.46 / Chapter 5.11.2 --- "Characteristics and implications of g(3)(t1,t2)" --- p.47 / Chapter 6 --- Interval distribution function with random force models --- p.49 / Chapter 6.1 --- Impact collision model --- p.51 / Chapter 6.2 --- Modified diffusion model --- p.53 / Chapter 6.3 --- Difficulties in the calculation of g(2)(t) --- p.54 / Chapter 6.4 --- Kn as a measured quantity --- p.57 / Chapter 7 --- Conclusion --- p.59 / Chapter A --- Alternative derivation of k and higher order corrections --- p.62 / Chapter B --- Evaluation of integrals in the exponential --- p.70 / Chapter B.1 --- Integral of the form ∫ts + ∫vu --- p.70 / Chapter B.2 --- Integrals of the form ∫ts + ∫vu + ∫yz --- p.72 / Chapter C --- Evaluation of four-click events --- p.74 / Bibliography --- p.76

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