統計力學（二）
Statistical Mechanics (II)
| 節 | 週三 |
|---|---|
7 15:30–16:20 | 統計力學（二） SC162 3 節連堂 |
8 16:30–17:20 | |
9 17:30–18:20 |
* 根據陽明交大上課時間表所列
"Statistical Physics II" course ventures into the rich possible behavior of complex and many-body systems responding to external influences, undergoing collective ordering via phase transitions, exhibiting universal scaling phenomena, and evolving under non-equilibrium conditions. A cornerstone of this advanced understanding is Mean Field Theory, which, despite its approximations, provides an invaluable first step and conceptual framework for understanding phase transitions and spontaneous symmetry breaking. To move beyond mean-field approximations and to systematically incorporate fluctuations, particularly near critical points, the course introduces Statistical Field Theory. This powerful approach reformulates statistical mechanics problems in the language of quantum field theory, enabling the use of tools like Functional Integrals. Functional integration provides a versatile and elegant method for averaging over microscopic degrees of freedom, calculating partition functions, and deriving effective theories for collective modes. Field-theoretic methodologies are indispensable for a comprehensive grasp of Linear Response Theory, which relates microscopic fluctuations to macroscopic observables, and for the precise application of the Renormalization Group (RG). The RG, consequently, offers profound insights into universality, scaling, and the characteristics of continuous phase transitions. Furthermore, the course introduces Non-equilibrium Statistical Physics, extending these equilibrium frameworks to systems subjected to external forces or those not yet thermalized. Expertise in these integrated topics is critical for researchers in fields such as condensed matter physics and materials science, providing the essential theoretical apparatus for analyzing diverse phenomena, interpreting experiments, developing models, and contributing to contemporary physics.
Statistical Physics I
Homework and lass participation: 50 % Final Exam: 50 %
| 週次 | 主題 |
|---|---|
| 第 1 週 | Brief review of Statistical Physics I, free quantum gases, thermodynamic stability conditions |
| 第 2 週 | Landau Theory: Mean-field theory for phase transitions, 1st order vs. continuous transitions, order parameter, coupled order parameter, critical exponents |
| 第 3 週 | The Ising model in one and two dimensions: exact solutions and mean field, high- and low T expansions, discrepancy between mean field and true critical exponents, scaling laws |
| 第 4 週 | The approach to Equilibrium: response functions, linear response theory, fluctuation-dissipation theorem |
| 第 5 週 | The Approach to Equilibrium II: Langevin equation |
| 第 6 週 | The Approach to Equilibrium III: Fokker-Planck equation, Boltzmann equation |
| 第 7 週 | The Approach to Equilibrium IV: H-theorem, Dissipatio, etc. |
| 第 8 週 | Kadanoff block spin method and real space scaling |
| 第 9 週 | Functional Integrals, Gaussian integrals, source terms, correlation functions, regularization |
| 第 10 週 | Ginzburg-Landau theory, \phi^4 theory, effective action |
| 第 11 週 | The renormalization group I: scaling and relevant, irrelevant and marginal fields; fixed points |
| 第 12 週 | The renormalization group II: RG flow, \epsilon-expansion, marginal dimension, Ginzburg-Wilson-Fisher fixed point |
| 第 13 週 | The renormalization group III: loop expansion, dangerously irrelevant operators, mean field exponents, hyper-scaling relations |
| 第 14 週 | The renormalization group IV: conformal invariance |
| 第 15 週 | Quantum phase transitions and the dynamical exponent z |
| 第 16 週 | Statistical physics of machine learning |
John Cardy: Scaling and renormalization in statistical physics Nigel Goldenfeld: Lectures on Phase Transitions and the Renormalization Group Daniel Amit: Field Theory, the Renormalization Group and Critical Phenomena
- 時間
- By appointment
- 聯絡方式
- kirchner@nycu.edu.tw