Lu, Wenlong = 一维光格子中费米型原子混合物基态行为的玻色化研究 / 魯文龙. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2009. / Includes bibliographical references (p. 70-72). / Abstract also in Chinese. / Lu, Wenlong = Yi wei guang ge zi zhong Feimi xing yuan zi hun he wu ji tai xing wei de Bose hua yan jiu / Lu Wenlong. / Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- Cold-atom systems --- p.1 / Chapter 1.1.1 --- Optical lattices --- p.2 / Chapter 1.1.2 --- Feshbach resonance --- p.3 / Chapter 1.2 --- Outline of the thesis --- p.6 / Chapter 2 --- Bosonization method --- p.8 / Chapter 2.1 --- Special property of one-dimensional Fermion system --- p.9 / Chapter 2.2 --- Bosonization techniques --- p.13 / Chapter 2.2.1 --- Density operators as bosonic fields --- p.14 / Chapter 2.2.2 --- Bosonization Identities --- p.17 / Chapter 2.3 --- Renormalization analysis for Sine-Gordon field --- p.19 / Chapter 2.4 --- Summary --- p.25 / Chapter 3 --- Mass imbalance in the spin polarized fermion system --- p.26 / Chapter 3.1 --- Kinetic term --- p.29 / Chapter 3.2 --- Interaction term --- p.32 / Chapter 3.3 --- Phase separation --- p.38 / Chapter 3.4 --- Dominant order and pairing behavior --- p.47 / Chapter 3.5 --- Summary --- p.49 / Chapter 4 --- Mass imbalance in the strong repulsive interaction region --- p.50 / Chapter 4.1 --- Effective Hamiltonian at large U limit --- p.50 / Chapter 4.2 --- Bosonization of t-J-Jz model --- p.54 / Chapter 4.3 --- Phase separation --- p.60 / Chapter 4.4 --- Summary --- p.67 / Chapter 5 --- Conclusions --- p.68 / Bibliography --- p.70 / Chapter A --- Proofs of Bosonization --- p.73 / Chapter A.1 --- Anti-commutation relations between two branches of fermionic field operators --- p.73 / Chapter A.2 --- Bosonization-identities checking --- p.74 / Chapter B --- Diagonalization of Quadratic Hamiltonian with Two Bosonic Fields --- p.77 / Chapter C --- Correlation functions --- p.82

Chung, Chun Kit = 超低溫相互作用費米原子中配對的探究 / 鍾俊傑. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2010. / Includes bibliographical references (leaves 81-88). / Abstracts in English and Chinese. / Chung, Chun Kit = Chao di wen xiang hu zuo yong fei mi yuan zi zhong pei dui de tan jiu / Zhong Junjie. / Chapter 1 --- Introduction --- p.1 / Chapter 2 --- Review on BCS theory --- p.4 / Chapter 2.1 --- BCS theory in uniform systems --- p.4 / Chapter 2.1.1 --- Hamiltonian and ground state solutions --- p.4 / Chapter 2.1.2 --- Choice of interaction potential --- p.7 / Chapter 2.1.3 --- Uniform atomic gas at T = 0 --- p.9 / Chapter 2.2 --- Self-consistent field method --- p.13 / Chapter 2.2.1 --- Population imbalanced systems --- p.17 / Chapter 2.3 --- Description of BCS states at finite temperatures --- p.22 / Chapter 3 --- Bipartite quantum entanglement in BCS states --- p.25 / Chapter 3.1 --- Mixed state bipartite quantum entanglement --- p.26 / Chapter 3.1.1 --- PPT criterion --- p.27 / Chapter 3.1.2 --- Negativity of p --- p.28 / Chapter 3.1.3 --- Entanglement witness --- p.30 / Chapter 3.1.4 --- Two-particle density matrix and two-body negativity --- p.30 / Chapter 3.2 --- Opposite spin states as subsystems --- p.31 / Chapter 3.2.1 --- Structure of and the negativity --- p.32 / Chapter 3.2.2 --- Relationship between the negativity and the order pa- rameter --- p.33 / Chapter 3.2.3 --- Distribution of negative eigenvalues of --- p.34 / Chapter 3.2.4 --- Constructing entanglement witness operator --- p.35 / Chapter 3.2.5 --- Remark: Same spin state as subsystems --- p.37 / Chapter 3.3 --- Momentum states as subsystems --- p.40 / Chapter 3.3.1 --- A and B as opposite momentum states --- p.41 / Chapter 3.3.2 --- A and B as different momentum states k and k' with k≠± k' --- p.43 / Chapter 3.3.3 --- A and B as the same momentum state --- p.44 / Chapter 3.4 --- Summary --- p.45 / Chapter 4 --- Radio-frequency spectroscopy --- p.47 / Chapter 4.1 --- The model Hamiltonian and dynamical equations --- p.49 / Chapter 4.1.1 --- Time-dependent variational method --- p.50 / Chapter 4.1.2 --- Time-dependent Bogoliubov-de Gennes equations --- p.51 / Chapter 4.2 --- Short-time dynamics --- p.53 / Chapter 4.2.1 --- Eigenvectors and Eigenvalues of C --- p.54 / Chapter 4.2.2 --- Build up of particle number density n3 and order param- eter Δ23 --- p.57 / Chapter 4.3 --- Summary --- p.61 / Chapter 5 --- Pairing in three-component systems --- p.63 / Chapter 5.1 --- The mean-field Hamiltonian --- p.64 / Chapter 5.2 --- Symmetric systems --- p.67 / Chapter 5.2.1 --- Quasiparticle spectra --- p.68 / Chapter 5.2.2 --- "Occupation number, condensation amplitude, and co- herence amplitude" --- p.70 / Chapter 5.2.3 --- Strengths of Ω --- p.71 / Chapter 5.3 --- Pairing in asymmetric systems --- p.73 / Chapter 5.3.1 --- Quasiparticle spectra and mean-field solutions --- p.73 / Chapter 5.3.2 --- Effects of Ωij --- p.74 / Chapter 5.4 --- Summary --- p.76 / Chapter 6 --- Conclusion and outlook --- p.79 / Bibliography --- p.81 / Chapter A --- Regularization techniques --- p.89 / Chapter B --- Wick's theorem --- p.91 / Chapter C --- Analytic solutions to three-component symmetric systems --- p.94