本論文包含兩個主題。第一部分研究無旋轉波近似下幾種原子與光的相互作用。第二部分研究駐波場耦合的電磁自感透明系統的反射和透射。它們的簡介如下。 / 第一部分。旋轉波近似即忽略掉原子與光相互作用哈密頓量中的反旋轉波項。它的有效性來自於能量守恆定律。但是在時間尺度非常小的情況下，根據海森堡不確定性原理，能量的不確定性可以很大，所以旋轉波近似不能應用于短時間行為的研究，比如量子芝諾和反芝諾效應，蘭姆位移，非共振極化以及超輻射和亞輻射中的能移。為超越旋轉波近似，我們對哈密頓量採用了么正變換。在變換之後的基矢之間，只有由帶修正係數的旋轉波項造成的躍遷。 / 我們從原子和真空的相互作用開始。對於氫原子來說，自由真空中沒有量子反芝諾效應，但是如果對真空態密度用腔或特異性材料做一些調製，量子反芝諾效應就會出現，蘭姆位移也會改變。我們接著研究原子和非真空光場的相互作用。我們計算了滿足光學定理的兩能級原子極化率。然後我們把么正變換用到了兩個全同原子和真空的相互作用，並計算了超輻射和亞輻射的輻射譜以及量子芝諾和反芝諾效應。 / 第二部分。在電磁自感透明系統裏，如果耦合光場為駐波，介質的極化率就會受到週期性調製而形成一維光子晶體。和傳統的傳輸矩陣不同的是，我們採用了麥克斯韋-劉維爾耦合波方程來處理這個系統並得到了光子晶體能帶的一個新的評判標準。起關鍵作用的物理量為非線性耦合係數除以波矢錯差和線性極化率的和，也就是非線性因素除以線性因素。 / 首先，我們研究了光子能帶的位置和寬度與實驗參數的量化關係。然後我們研究了溫度升高时光子晶體的融化以及向多普勒無關的多波混頻的轉化。如果在兩束對向傳播的耦合場之間引入失諧，駐波場的包絡會形成一個“飛行“的光子晶體。因為多普勒效應，順著飛行方向或者逆著飛行方向的探測光在一維光子晶體的坐標系裏具有不同的頻率。在靜止坐標系看，透射譜會在頻率上錯開並形成光學二極體。 / This thesis includes two topics. Part 1 is on the various atom-photon interactions without rotating-wave approximation (RWA). Part 2 is on the reflection and transmission in a standing wave coupled electromagnetically induced transparency (EIT) system. / Part 1. In the RWA, the counter-rotating terms in the atom-photon interaction Hamiltonian are neglected. Its validity is the result of energy conservation. However, if the time scale is sufficiently small, the uncertainly in the energy can become large, according to the Heisenberg uncertainty principle. Thus the RWA can not be applied in the study of the short time behavior, such as the quantum Zeno effect (QZE) and anti-Zeno effect (QAZE), the Lamb shift, the non-resonant polarizability and shifts in the superradiance and subradiance. To go beyond RWA, we apply a unitary transformation on the Hamiltonian. In the transformed basis, there are only secular transitions due to rotating terms with modified coupling constants. / We start from the interactions between atom and vacuum. For the hydrogen atom, there is no QAZE in free vacuum. However, with the modification in the density of states of the vacuum by a cavity or a meta-material, the QAZE appears and the Lamb shift changes. We then turn to the atom in light field, where the polarizability of a two-level atom is calculated and the results satisfy the optical theorem. The unitary transformation is then applied to two identical atoms interacting with vacuum. Their various emission spectra of the superradiance and subradiance and the QZE and QAZE are studied. / Part 2. In an EIT system, if the coupling field is a standing wave, the susceptibility of the medium is periodically modified to form a one-dimensional photonic crystal (1DPC). In contrast to the conventional treatment with transfer matrix, we use Maxwell-Liouville coupled-wave equations and propose new criteria for the bandgap of the photonic crystal (PC). The relevant quantity is the ratio between the nonlinear coupling coefficient and the wave vector mismatch plus the linear susceptibility, which is the nonlinear effect over the linear effect. / First, we study the quantitative relation between the position and width of the photonic bandgap and the experimental parameters. We then show that, as the temperature rises, the 1DPC melts down and enters the Doppler-free wave-mixing regime. By introducing detuning between the two counter-propagating fields in the standing wave, we make the envelope of the standing wave move and form a ‘flying’ 1DPC. Owing to the Doppler Effect, the probe fields propagating along with or counter to the moving direction have different frequencies in the 1DPC frame. In the rest frame, the transmission spectra in two directions are thus shifted with respect to each other and we obtain an optical diode. / Detailed summary in vernacular field only. / Detailed summary in vernacular field only. / Detailed summary in vernacular field only. / Detailed summary in vernacular field only. / Detailed summary in vernacular field only. / Wang, Dawei = 無旋轉波近似下原子-光子相互作用和駐波耦合的電磁自感透明系統 / 王大偉. / Thesis (Ph.D.)--Chinese University of Hong Kong, 2012. / Includes bibliographical references (leaves 128-135). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Abstract also in Chinese. / Wang, Dawei = Wu xuan zhuan bo jin si xia yuan zi-guang zi xiang hu zuo yong he zhu bo ou he de dian ci zi gan tou ming xi tong / Wang Dawei. / Abstract --- p.iv / Acknowledgements --- p.vii / Table of Contents --- p.xi / List of Figures --- p.xiii / Chapter Part 1 --- Atom-photon interactions without rotating-wave approximation --- p.1 / Chapter Chapter 1 --- Introduction on atom-photon interactions --- p.2 / Chapter 1.1 --- Spontaneous emission --- p.2 / Chapter 1.2 --- Quantum Zeno and anti-Zeno effect --- p.8 / Chapter 1.3 --- Rotating-wave approximation --- p.10 / Chapter 1.4 --- Go beyond the rotating-wave approximation --- p.12 / Chapter 1.5 --- Non-dynamic Lamb shift --- p.15 / Chapter 1.6 --- Summary --- p.17 / Chapter Chapter 2 --- QZE, QAZE and Lamb shift in vacuum --- p.18 / Chapter 2.1 --- Introduction --- p.18 / Chapter 2.2 --- QZE in the free vacuum --- p.19 / Chapter 2.3 --- QAZE in modified vacuum --- p.21 / Chapter 2.4 --- Time Evolution of the Lamb Shift --- p.25 / Chapter 2.5 --- The Lamb shift in modified vacuum --- p.30 / Chapter 2.6 --- Summary --- p.35 / Chapter Chapter 3 --- Atom in light: polarizability and scattering --- p.37 / Chapter 3.1 --- Introduction --- p.37 / Chapter 3.2 --- The polarizability of a two-level atom without RWA --- p.39 / Chapter 3.3 --- The optical theorem --- p.43 / Chapter 3.4 --- The effects of the counter rotating terms --- p.46 / Chapter 3.5 --- The frequency shift --- p.48 / Chapter 3.6 --- Summary --- p.50 / Chapter Chapter 4 --- Spontaneous emission of two identicalatoms --- p.51 / Chapter 4.1 --- Introduction --- p.51 / Chapter 4.2 --- Unitary transform of the Hamiltonian --- p.52 / Chapter 4.3 --- Dynamicevolution --- p.57 / Chapter 4.4 --- Decay rates, Lamb shift and emission spectrum in the longtime limit --- p.59 / Chapter a) --- The decayrates --- p.59 / Chapter b) --- The Lamb shift --- p.60 / Chapter c) --- The emission spectra --- p.62 / Chapter 4.5 --- Short time evolution --- p.68 / Chapter 4.6 --- Summary --- p.70 / Chapter Appendix --- the shifts and decay rates of the symmetric and anti-symmetric states --- p.71 / Chapter Part 2 --- Standing wave coupled electromagnetically induced transparency system --- p.74 / Chapter Chapter 5 --- Introduction on electromagnetically induced transparency --- p.75 / Chapter 5.1 --- The electromagnetically induced transparency --- p.75 / Chapter 5.2 --- The susceptibilities of SWEIT --- p.81 / Chapter 5.3 --- Summary --- p.86 / Chapter Appendix --- the recursion relation and the proof of Eq.(212) --- p.86 / Chapter Chapter 6 --- From photonic crystal to Doppler-free wave-mixing --- p.90 / Chapter 6.1 --- Introduction --- p.90 / Chapter 6.2 --- The Maxwell-Liouville equations --- p.91 / Chapter 6.3 --- The photonic bandgaps --- p.93 / Chapter 6.4 --- The meltdown of the photonic crystal and the pulse matching --- p.99 / Chapter 6.5 --- Summary --- p.106 / Chapter Appendix A --- the Maxwell-Liouville equation --- p.106 / Chapter Appendix B --- a new criterion of photonic band-gaps --- p.109 / Chapter Chapter 7 --- The optical-diode by a flying photonic crystal --- p.112 / Chapter 7.1 --- Introduction --- p.112 / Chapter 7.2 --- Coupled-wave equations of the ‘flying’ photonic crystal --- p.113 / Chapter 7.3 --- The spectra of the optical diode --- p.118 / Chapter 7.4 --- The influence of the experimental parameters --- p.120 / Chapter 7.5 --- Summary --- p.126 / CURRICULUM VITAE --- p.136

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

No description available.

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.

No description available.

abstract: The rigidity of a material is the property that enables it to preserve its structure when deformed. In a rigid body, no internal motion is possible since the degrees of freedom of the system are limited to translations and rotations only. In the macroscopic scale, the rigidity and response of a material to external load can be studied using continuum elasticity theory. But when it comes to the microscopic scale, a simple yet powerful approach is to model the structure of the material and its interparticle interactions as a ball$-$and$-$spring network. This model allows a full description of rigidity in terms of the vibrational modes and the balance between degrees of freedom and constraints in the system. In the present work, we aim to establish a microscopic description of rigidity in \emph{disordered} networks. The studied networks can be designed to have a specific number of degrees of freedom and/or elastic properties. We first look into the rigidity transition in three types of networks including randomly diluted triangular networks, stress diluted triangular networks and jammed networks. It appears that the rigidity and linear response of these three types of systems are significantly different. In particular, jammed networks display higher levels of self-organization and a non-zero bulk modulus near the transition point. This is a unique set of properties that have not been observed in any other types of disordered networks. We incorporate these properties into a new definition of jamming that requires a network to hold one extra constraint in excess of isostaticity and have a finite non-zero bulk modulus. We then follow this definition by using a tuning by pruning algorithm to build spring networks that have both these properties and show that they behave exactly like jammed networks. We finally step into designing new disordered materials with desired elastic properties and show how disordered auxetic materials with a fully convex geometry can be produced. / Dissertation/Thesis / Doctoral Dissertation Physics 2018

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