Chan David. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2000. / Includes bibliographical references (leaves [73]-76). / Abstracts in English and Chinese. / Abstract --- p.i / Acknowledgement --- p.ii / Contents --- p.iii / List of Figures --- p.vi / List of Tables --- p.viii / Chapter Chapter 1. --- Introduction --- p.1 / Chapter Chapter 2. --- Relaxation Phenomena --- p.8 / Chapter 2.1 --- Introduction --- p.8 / Chapter 2.2 --- Relaxation Phenomena --- p.8 / Chapter 2.3 --- Ising Model as an Example --- p.9 / Chapter 2.3.1 --- Monte Carlo Simulation --- p.10 / Chapter 2.3.2 --- Transition Matrix Method --- p.11 / Chapter 2.3.3 --- Results and Comparison --- p.13 / Chapter 2.4 --- Conclusion --- p.17 / Chapter Chapter 3. --- Stochastic Processes --- p.18 / Chapter 3.1 --- Introduction --- p.18 / Chapter 3.2 --- Stochastic Processes --- p.18 / Chapter 3.3 --- Markov Processes and Markov Chains --- p.19 / Chapter 3.4 --- Transition Matrix --- p.20 / Chapter 3.5 --- Detailed Balance Condition --- p.21 / Chapter 3.5.1 --- Weaker Balance Condition --- p.22 / Chapter 3.6 --- Ergodicity --- p.22 / Chapter 3.7 --- Conclusion --- p.23 / Chapter Chapter 4. --- Master Equation --- p.24 / Chapter 4.1 --- Introduction --- p.24 / Chapter 4.2 --- Master Equation --- p.24 / Chapter 4.3 --- Properties of the Transition Matrix W --- p.25 / Chapter 4.4 --- Eigenvalue Equation --- p.26 / Chapter 4.5 --- Relaxation Time --- p.28 / Chapter 4.6 --- Properties of Eigenvalues and Eigenvectors --- p.29 / Chapter 4.7 --- Power Method --- p.32 / Chapter 4.7.1 --- Power Method for λx --- p.33 / Chapter 4.7.2 --- Power Method for λx --- p.35 / Chapter 4.7.3 --- Power Method for λ2 of W --- p.38 / Chapter 4.8 --- Conclusion --- p.39 / Chapter Chapter 5. --- Decimation --- p.40 / Chapter 5.1 --- Introduction --- p.40 / Chapter 5.2 --- Method of Decimation --- p.40 / Chapter 5.2.1 --- Exact Formalism --- p.42 / Chapter 5.2.2 --- Iterative Formalism --- p.44 / Chapter 5.2.3 --- Approximate Formalism --- p.46 / Chapter 5.3 --- Decimation as an Effective Master Equation --- p.46 / Chapter 5.4 --- One Dimensional Energy Landscape --- p.47 / Chapter 5.5 --- Conclusion --- p.58 / Chapter Chapter 6. --- Mean Field Theory --- p.59 / Chapter 6.1 --- Introduction --- p.59 / Chapter 6.2 --- Toy Model A --- p.59 / Chapter 6.3 --- Toy Model B --- p.61 / Chapter 6.4 --- Mean Field Theory : a Lower Bound of Relaxation Time --- p.62 / Chapter 6.5 --- Mean Field Theory with the Decimation Formalism --- p.62 / Chapter 6.6 --- Mean Field Theory with Fluctuations --- p.63 / Chapter 6.6.1 --- Fluctuation Phenomena with the Decimation Formalism --- p.67 / Chapter 6.7 --- Conclusion --- p.69 / Chapter Chapter 7. --- Conclusion --- p.70 / Bibliography --- p.73
| Identifer | oai:union.ndltd.org:cuhk.edu.hk/oai:cuhk-dr:cuhk_323164 |
| Date | January 2000 |
| Contributors | Chan, David., 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, vii, 76 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/) |
Page generated in 0.0019 seconds