Lau Wai Chuen. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1997. / Includes bibliographical references (leaves 93-94). / Lau Wai Chuen. / Contents --- p.ii / List of Figures --- p.iv / List of Tables --- p.vi / Abstract --- p.ix / Acknowledgement --- p.x / Chapter Chapter 1. --- Introduction --- p.1 / Chapter 1.1 --- Superconductivity --- p.1 / Chapter 1.2 --- The Hubbard model and the Extended Hubbard model --- p.3 / Chapter 1.3 --- Gap Equation --- p.6 / Chapter 1.3.1 --- One-dimensional solutions --- p.11 / Chapter 1.3.2 --- Two-dimensional solutions --- p.12 / Chapter Chapter 2. --- Solving BCS equation --- p.15 / Chapter 2.1 --- Zero value of the denominator of the BCS equations --- p.15 / Chapter 2.2 --- Discontinuity of the BCS equations --- p.16 / Chapter Chapter 3. --- Results of BCS equations for finite size clusters --- p.34 / Chapter 3.1 --- Method used to solve BCS equations --- p.34 / Chapter 3.2 --- Results for the one dimensional and two dimensional lattices --- p.34 / Chapter 3.2.1 --- Extended S-wave solution --- p.35 / Chapter 3.2.2 --- P-wave and D-wave solutions --- p.36 / Chapter Chapter 4. --- Results of BCS equations compare with exact solutions --- p.69 / Chapter 4.1 --- "An exact solution of D-wave, Ne=2" --- p.69 / Chapter 4.2 --- Comparison of the ground state energy with the results calculated by exact diagonalization --- p.73 / Chapter Chapter 5. --- The Phase Diagram of the superconducting state --- p.78 / Chapter Chapter 6. --- Conclusion --- p.91 / Bibliography --- p.93

Tam Ka Ming. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2002. / Includes bibliographical references (leaves 142-145). / Text in English; abstracts in English and Chinese. / Tam Ka Ming. / Acknowledgement --- p.ii / Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- Models for Many Body Systems --- p.1 / Chapter 1.2 --- High Temperature Superconductor --- p.5 / Chapter 1.3 --- Reasons of Study Double Layers --- p.9 / Chapter 1.4 --- "Incommensurate Magnetic Excitation, Order Parameters" --- p.10 / Chapter 1.5 --- Thesis Organization --- p.10 / Chapter 2 --- Monte Carlo Methods --- p.12 / Chapter 2.1 --- General Aspects of Monte Carlo Simulation --- p.12 / Chapter 2.2 --- "Markov Chain, Metropolis Algorithm, Heat-Bath Algorithm" --- p.18 / Chapter 2.3 --- Quantum Monte Carlo --- p.21 / Chapter 2.4 --- Variational Quantum Monte Carlo --- p.22 / Chapter 2.5 --- Green Function Monte Carlo --- p.27 / Chapter 2.6 --- Auxiliary Field Monte Carlo --- p.35 / Chapter 2.7 --- Summary of Quantum Monte Carlo --- p.38 / Chapter 3 --- Constrained Path Monte Carlo --- p.40 / Chapter 3.1 --- Various Formulas Used in Constrained Path Monte Carlo --- p.40 / Chapter 3.2 --- Constrained Path Monte Carlo --- p.47 / Chapter 3.3 --- Constrained Path Approximation --- p.51 / Chapter 3.4 --- Measurements --- p.52 / Chapter 3.5 --- Method of Avoiding Numerical Instability --- p.55 / Chapter 4 --- Parallelisation of CPMC Program --- p.57 / Chapter 4.1 --- Architecture of Parallel Machine --- p.57 / Chapter 4.2 --- Communication Methods in Parallel Program --- p.65 / Chapter 4.3 --- Comparison of Parallel and Serial Program --- p.74 / Chapter 4.4 --- Measure of Parallel Program --- p.85 / Chapter 4.5 --- Analysis of Serial CPMC Program --- p.89 / Chapter 4.6 --- Analysis of the Parallel CPMC Program --- p.93 / Chapter 5 --- Results from CPMC --- p.101 / Chapter 5.1 --- Hubbard Model with Next Nearest Neighbour Hopping --- p.101 / Chapter 5.2 --- Spin and Charge Correlations --- p.104 / Chapter 5.3 --- Vertex Contributions --- p.111 / Chapter 6 --- Mean Field Calculations of bilayer --- p.119 / Chapter 6.1 --- Objective --- p.119 / Chapter 6.2 --- Theoretical Model --- p.121 / Chapter 6.3 --- Method of Solving the Model --- p.122 / Chapter 6.4 --- Finding Susceptibility by RPA --- p.131 / Chapter 6.5 --- Results --- p.136 / Chapter 6.6 --- Summary --- p.140 / Chapter 7 --- Summary --- p.141 / Bibliography --- p.142