Liang zi li xue zhong zhi jiu chan

Ku, Wai Lim.Thesis (M.Phil.)--Chinese University of Hong Kong, 2008.Includes bibliographical references (leaves 97-100).Abstracts in English and Chinese.Ku, Wai Lim.Chapter 1 --- Review of Entanglement --- p.1Chapter 1.1 --- Schmidt Decomposition --- p.1Chapter 1.1.1 --- Schmidt Decomposition in Continuous Systems --- p.3Chapter 1.2 --- Detecting the Quantum Entanglement of Pure States --- p.5Chapter 1.3 --- Quantifying the Quantum Entanglement of Pure States --- p.6Chapter 1.3.1 --- Von Neumann entropy --- p.8Chapter 1.3.2 --- Purity --- p.8Chapter 1.3.3 --- Logarithmic Negativity --- p.9Chapter 1.3.4 --- Concurrence --- p.10Chapter 2 --- Review of Entanglement in the Relativistic Framework --- p.11Chapter 2.1 --- Lorentz Transformation of a Quantum State --- p.11Chapter 2.2 --- Unruh effect --- p.14Chapter 2.2.1 --- The Rindler Spacetime --- p.14Chapter 2.2.2 --- Quantum field theory in Rindler Spacetime --- p.18Chapter 2.2.3 --- Lightcone Mode Expansion --- p.21Chapter 2.3 --- Entanglement Measured by Uniformly Accelerating Detectors --- p.25Chapter 2.3.1 --- Number of States in Rindler Spacetime --- p.26Chapter 2.3.2 --- Entanglement in an non-inertial frame --- p.29Chapter 2.4 --- Entanglement in an Expanding Universe --- p.32Chapter 2.5 --- Summary --- p.36Chapter 3 --- Some Topics in Entanglement --- p.37Chapter 3.1 --- Introduction --- p.37Chapter 3.2 --- Accelerating Schrodinger particles --- p.40Chapter 3.3 --- Entanglement of Two-body Wavefuction --- p.43Chapter 3.4 --- Accelerating the Relativistic Particles --- p.47Chapter 3.4.1 --- Quantization of Fields --- p.47Chapter 3.5 --- Accelerating Fermions --- p.51Chapter 3.6 --- Accelerating scalar particles --- p.55Chapter 3.6.1 --- Spectrum --- p.55Chapter 3.6.2 --- Entanglement --- p.55Chapter 3.6.3 --- Entanglements if the Number of Produced Pairs is Restricted --- p.57Chapter 3.7 --- Discussion of the Accelerating Particles --- p.60Chapter 3.8 --- Entanglement in de Sitter space --- p.63Chapter 3.8.1 --- Pair Creation in de Sitter space --- p.63Chapter 3.8.2 --- Entanglement in the de Sitter space --- p.65Chapter 4 --- Review of Geometric Phase --- p.67Chapter 4.1 --- Magnetic Aharonov-Bohm Effect --- p.68Chapter 4.2 --- Berry Phase --- p.69Chapter 4.3 --- Aharonov-Anandan Phase --- p.72Chapter 4.4 --- Pancharatnam Phase --- p.73Chapter 4.5 --- Geometric Phase in a two-level atom --- p.75Chapter 5 --- Relationship Between Entanglement and Geometric Phase --- p.78Chapter 5.1 --- Relationship Between Berry's Phase and Concurrence --- p.78Chapter 5.2 --- Jaynes-Cummings model --- p.82Chapter 5.3 --- Projective Phase in the Jaynes-Cummings model --- p.86Chapter A --- The Bogoliubov coefficients in the scalar case --- p.91Chapter B --- Reducing the Dirac equations to two Klein-Gordon equations --- p.94Bibliography --- p.9