Wong Hon Man = 量子力學中之幾何相位 / 黃漢文. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2005. / Includes bibliographical references (leaves 75-78). / Text in English; abstracts in English and Chinese. / Wong Hon Man = Liang zi li xue zhong zhi ji he xiang wei / Huang Hanwen. / Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- Geometric Phase in Orthogonal States --- p.2 / Chapter 1.2 --- Projective Phase --- p.3 / Chapter 1.3 --- Bose-Einstein Condensate --- p.3 / Chapter 1.4 --- Arrangement of the Thesis --- p.3 / Chapter 2 --- Review of Geometric Phase --- p.5 / Chapter 2.1 --- Introduction --- p.5 / Chapter 2.2 --- Berry's Phase --- p.6 / Chapter 2.3 --- Aharonov-Anadan Phase --- p.9 / Chapter 2.4 --- Pancharatnam Phase --- p.10 / Chapter 2.5 --- Example of a Two-State System --- p.13 / Chapter 2.6 --- Remark on Phase Factor --- p.15 / Chapter 3 --- Review of Geometric Phase near Orthogonal States --- p.16 / Chapter 3.1 --- π Phase Change --- p.17 / Chapter 3.2 --- Off-diagonal Geometric Phase --- p.18 / Chapter 4 --- Projective Phase --- p.21 / Chapter 4.1 --- Projective Measurement --- p.21 / Chapter 4.2 --- Definition in Differential Geometry --- p.22 / Chapter 4.3 --- Gauge Transformation --- p.24 / Chapter 4.4 --- Two-state System and Monopole --- p.26 / Chapter 5 --- π Phase Change --- p.30 / Chapter 5.1 --- Projective Phase near Orthogonal States --- p.30 / Chapter 5.2 --- Two-state system --- p.32 / Chapter 5.3 --- Three-state systems --- p.33 / Chapter 5.4 --- Topological restriction for Spin-1 System --- p.36 / Chapter 5.5 --- Remark on Continuity of Curves --- p.37 / Chapter 6 --- Topological Number Associated with Projective Phase --- p.38 / Chapter 6.1 --- Curves Separated by Zero Dot Products --- p.38 / Chapter 6.2 --- Definition of Phase without 2π arbitrary phase --- p.41 / Chapter 6.3 --- 1st Chern Number Associated with Closed Loops --- p.42 / Chapter 6.4 --- Example with a Spin-m System --- p.43 / Chapter 6.5 --- πphase change --- p.45 / Chapter 6.6 --- Variation of Projection States and Curves --- p.46 / Chapter 7 --- Off-diagonal geometric phase --- p.50 / Chapter 7.1 --- Experiment to Measure Projective Phase --- p.52 / Chapter 8 --- Summary on Geometric Phase near Orthogonal States --- p.53 / Chapter 9 --- Review of Bose-Einstein Condensate --- p.55 / Chapter 9.1 --- Gross-Pitaevskii Equation --- p.55 / Chapter 9.2 --- One-Dimensional GP equation --- p.57 / Chapter 9.3 --- Elementary Excitations --- p.57 / Chapter 10 --- Geometric Phase in Bose-Einstein Condensate --- p.59 / Chapter 10.1 --- Two-state Geometric Phase --- p.59 / Chapter 10.2 --- Geometric Phase in Perturabation --- p.60 / Chapter 10.3 --- Numerical Results --- p.63 / Chapter 10.4 --- Discussions --- p.64 / Chapter A --- Monopole --- p.69 / Chapter B --- Definition of Fibre Bundle --- p.71 / Chapter C --- Evaluation of Bargmann invariant by Pancharatnam Phase Formula --- p.73 / Bibliography --- p.75
| Identifer | oai:union.ndltd.org:cuhk.edu.hk/oai:cuhk-dr:cuhk_325422 |
| Date | January 2005 |
| Contributors | Wong, Hon Man., Chinese University of Hong Kong Graduate School. Division of Physics. |
| Source Sets | The Chinese University of Hong Kong |
| Language | English, Chinese |
| Detected Language | English |
| Type | Text, bibliography |
| Format | print, x, 78 leaves : ill. ; 30 cm. |
| Rights | Use of this resource is governed by the terms and conditions of the Creative Commons “Attribution-NonCommercial-NoDerivatives 4.0 International” License (http://creativecommons.org/licenses/by-nc-nd/4.0/) |
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