Duo ti xi tong zhong de liang zi xiang bian dong li xue

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.1Chapter 1.1 --- Quantum phase transitions --- p.1Chapter 1.2 --- Schemes detecting QPTs --- p.3Chapter 1.2.1 --- Traditional schemes --- p.3Chapter 1.2.2 --- Quantum Entanglement --- p.4Chapter 1.2.3 --- Quantum fidelity --- p.4Chapter 1.2.4 --- Loschmidt echoes --- p.5Chapter 1.2.5 --- Quench dynamics --- p.6Chapter 1.3 --- Motivation --- p.7Chapter 2 --- Theoretical framework --- p.9Chapter 2.1 --- Quantum Zeno effect --- p.9Chapter 2.2 --- Mathematical formulation --- p.11Chapter 2.3 --- Remarks --- p.14Chapter 3 --- Analysis on the One-dimensional Transverse-field Ising model --- p.17Chapter 3.1 --- The model --- p.17Chapter 3.2 --- Diagonalization of the Hamiltonian --- p.20Chapter 3.2.1 --- Jordan-Wigner transformation --- p.20Chapter 3.2.2 --- Fourier Transformation --- p.24Chapter 3.2.3 --- Bogoliubov transformation --- p.26Chapter 3.3 --- Quantum Zeno dynamics in the model --- p.28Chapter 3.3.1 --- Analytical calculation of the Zeno susceptibility --- p.28Chapter 3.3.2 --- Validity of the analytical result --- p.31Chapter 3.3.3 --- Scaling behavior of the Zeno susceptibility --- p.33Chapter 3.3.4 --- Zeno susceptibility around the critical point --- p.35Chapter 3.4 --- Conclusion and experimental outlook --- p.38Chapter 4 --- Analysis on the Lipkin-Meshkov-Glick Model --- p.40Chapter 4.1 --- The model --- p.41Chapter 4.2 --- Diagonalization of the Hamiltonian --- p.46Chapter 4.2.1 --- Holstein-Primakoff transformation --- p.46Chapter 4.2.2 --- Bogoliubov transformation --- p.49Chapter 4.3 --- Quantum Zeno dynamics in the model --- p.51Chapter 4.3.1 --- Analytical form of the Zeno susceptibility and its scaling behavior --- p.51Chapter 4.3.2 --- Validity of the analytical result --- p.54Chapter 4.3.3 --- Numerical analysis of the Zeno susceptibility --- p.55Chapter 4.4 --- Conclusion --- p.60Chapter 5 --- Analysis on the Kitaev model on a honeycomb lattice --- p.61Chapter 5.1 --- The model --- p.61Chapter 5.2 --- Diagonalization of the Hamiltonian --- p.63Chapter 5.2.1 --- Jordan-Wigner transformation for two-dimensional systems --- p.64Chapter 5.2.2 --- Majorana fermion representation --- p.68Chapter 5.2.3 --- Fermions on the 之-bonds --- p.71Chapter 5.2.4 --- Bogoliubov transformation --- p.73Chapter 5.3 --- Energy spectrum --- p.75Chapter 5.4 --- Quantum Zeno dynamics in the model --- p.77Chapter 5.4.1 --- Coupling along the Jx = Jy line --- p.77Chapter 5.4.2 --- Coupling along the line with constant Jz --- p.83Chapter 5.5 --- Conclusion --- p.90Chapter 6 --- Conclusion and outlook --- p.91Bibliography --- p.94Chapter A --- Perturbative form of the Loschimdt Echo --- p.100Chapter B --- Hellmann-Feynman theorem --- p.107Chapter C --- Commutation relations in the Jordan-Wigner transformation --- p.10