核心能力
Core Competencies
| ♠ | 中階物理知識 | 25 % |
| Middle level knowledge of physics | ||
| ♠ | 自主學習能力 | 25 % |
| Independent learning capability | ||
| ♠ | 物理相關數學能力 | 25% |
| Mathematical capability in physics | ||
| ♠ | 基礎物理知識 | 25 % |
| Basic level knowledge of physics |
課程說明
Brief course description
| ♠ | 盡信書不如無書。 – 孟子 |
| ♠ | 道可道，非常道。 – 老子 |
| Keep throwing out the inessential until the problem becomes trivial. Then go back one step. – Sam Edwards | |
| The quotes above are very elegant descriptions about the attitude of learning. If one completely believe what a book says, it is better not to read any books. Any books should not become an obstacles for thinking. The second quote says: if a principle can be explicitly described by words, such a principle will not be the eternal principle. Somehow they describe how our understanding evolves as a function of time. | |
| ♠ | This course will introduce students to one of the pillars of theoretical physics: Statistical Mechanics. Statistical mechanics provides a framework |
| to understand and describe all macroscopic systems, from a cooling cup of coffee, boiling water to electrons in metals, semiconductors, superconductors, magnets, black holes, … just to name a few. Statistical mechanics is a body of knowledge that establishes the relation between microscopic properties and macroscopic properties of the system, which is essential from both fundamental and application points of view. The course will cover the basic theoretical framework and applications(starting from non-interacting systems, classical gas, and quantum gases(fermions and bosons) . After the study of non-interacting systems, we will discuss the techniques related to interacting systems. |
致謝
Acknowledgement
| ♠ | Prof. Christopher Laumann : for allowing us to use the python tutorial scripts. |
指定用書
Text Books
| 1. | Statistical Mechanics in a Nutshell, Luca Peliti [Pel11]– Formal approach, might be a little bit boring. |
| 2. | Statistical Mechanics: Volume 5, Landau and Lifshitz – The classic theoretical physics collection.It’s unfortunate that |
| we cannot discuss with Landau anymore, but his way of thinking is left in the classic textbook series forever. It’s the textbook we used when I was a graduate student at CU Boulder. | |
| 3. | (2nd Edition)Statistical Mechanics: Entropy, Order Parameters, and Complexity: Second Edition (Oxford Master Series |
| in Physics), James P. Sethna [Set21]– More applications of statistical mechanics. When you have the question: why should we study statistical mechanics? You can find various interesting assignments at the end of each chapter. | |
參考用書
References
| 1. | Statistical mechanics, R. K. Pathria and P. D. Beale – A relatively formal but solid textbook. |
| 2. | Thermodynamics and an introduction to thermostatistics, H. B. Callen |
| – An excellent textbook that discusses the fundamental principles of thermodynamics. | |
| 3. | Statistical physics of particles/fields, M. Kardar |
| – A pair of modern textbooks about statistical physics with detailed discussion. | |
| 4. | Statistical mechanics, Shang-Keng Ma |
| – An idiosyncratic textbook that introduces statistical mechanics in the 70’s on this campus. (Originally written in Mandarin.) The textbook discusses the fundamentals and applications of statistical mechanics and exposes some of the thorny questions in the study of statistical mechanics that are not discussed in standard textbooks. | |
| 5. | Statistical mechanics, K. Huang NTU open course |
| ♠ | A good reference is the one that you are willing to read. |
課程大綱
Outline of the course
| 1. | Motivation and basic mathematical tools for statistical mechanics. |
| 2. | Random walks and universality classes |
| 3. | Thermodynamics as a phenomenological theory and the fundamental postulates of thermodynamics. |
| 4. | The fundamental postulates of statistical mechanics and connection with thermodynamics. |
| 5. | Applications of statistical mechanics on non-interacting systems |
| ☉ two-level system | |
| ☉ ideal gas model | |
| ☉ non-interacting boson/fermion | |
| 6. | Interacting systems and mean-field theory |
教學進度
Syllabus / Course plan
| Date | Week | Contents |
| 02.20 | W1 | (w1) Introduction – Thermodynamics, statistical mechanics and the concept of emergence. (Random walks, concept of the scaling invariance, and the universality class.) Readings: [Set21]: Chapter 1, Chapter 2; [Cal98]: Chapter 21; Online lecture notes: Fundamentals |
| 02.27 | W2 | (w2) Introduction – (Continue) Thermodynamics, statistical mechanics and the concept of emergence. (the diffusion equation: microscopic picture and the effective theory, basic probability theory.) Readings: [Set21]: Chapter 2; Online lecture notes: Random walks and emergent properties. Quiz 1: Random matrix theory |
| 03.06 | W3 | (w3) Statistical postulates and review of thermodynamics. (The ideal gas example and the formal structure of thermodynamics, Key properties of entropy. ) Readings: [Set21]: Chapter 2; Online lecture notes: Random walks and emergent properties. Quiz 2: Taylor series and asymptotic series |
| 03.13 | W4 | (w4) The fundamental postulates of statistical mechanics (The idea of phase space, observables, Boltzmann’s entropy formula, the idea of Liouville’s theorem) Readings: [Set21]: Chapter 3; [Pel11]: Chapter 2 and Chapter 3, Online lecture notes: Random walks and emergent properties and Thermodynamics and statistical mechanics Quiz 3: Generating random walks and the emergent symmetry |
| 03.20 | W5 | (w5) The fundamental postulates of statistical mechanics (Proof of Liouville’s theorem, variational principle of the entropy, quantum version of the Boltzmann’s postulate, the phase space of ideal gas, the microcanonical ensemble. ) Readings: [Set21]: Chapter 3; [Pel11]: Chapter 2 and Chapter 3, Online lecture notes: Thermodynamics and statistical mechanics and Postulates of statistical mechanics Quiz 4: Monte Carlo for |
| 03.27 | W6 | (w6) The fundamental postulates of statistical mechanics (The canonical ensemble, generalized ensemble, Grand canonical ensemble.) |
| 04.03 | W7 | (w7) Holiday |
| 04.10 | W8 | (w8) The midterm exam |
| 04.17 | W9 | (w9) The interacting free systems (Single mode harmonic oscillator, midterm exam discussion) |
| 04.24 | W10 | (w10) The interacting free systems (Fermions and bosons, quantum statistics, Hamiltonian and Hilbert space of many-particle systems, partition function and grand partition function for free fermions/bosons.) |
| 05.01 | W11 | (w11) The interacting free systems (Bose-Einstein and Fermi-Dirac distribution, Bose-Einstein condensate, Fermi gases, second quantization ) |
| 05.08 | W12 | (w12) The interacting free systems (second quantization, Goldstone theorem, phonon, photon) Phases and phase transitions (Motivation of the study of phases and phase transitions.) |
| 05.15 | W13 | (w13) Phases and phase transitions (Phases and phase diagram, thermodynamic limit, phase transitions, symmetry and spontaneous symmetry braking (I:Introduction), classical Ising model and the phase diagram ) |
| 05.22 | W14 | (w14) Phases and phase transitions ( The heuristic arguments of the phase diagram of Ising model, spontaneous symmetry breaking(II: Analytic property of free energy for finite and thermodynamic system).) |
| 05.29 | W15 | (w15) Phases and phase transitions ( Spontaneous symmetry breaking(III: Ergodicity breaking), the one-dimensional Ising model and the transfer matrix method, The Weiss mean field theory and the universality class, comparing Ising model and Van der Waals gas model, symmetry and the Ginsburg-Landau theory. ) |
| 06.05 | W16 | (w16) The final exam |
如何從課程中受益？
How to benefit from the course? The correct mindset: to pass the course is not difficult; to learn something requires hard work ! ♠ For students who want to work in theoretical physics: The bar for theoretical physics is high. It would help if you tried to learn statistical mechanics by self-studying the subject. Try to self-studying the two textbooks and discuss with classmates, TAs, and me during office hours for those important conceptual questions.
♠ The bar is also high for students who want to work in experimental physics: Try to connect statistical mechanics with experimental phenomena that you have learned. I will mention some examples. However, those examples are far from enough to build the physics intuition for an outstanding experimentalist.
♠ For students who do not belong to above-mentioned categories: The bar is even higher. Try to find out the possible use of statistical mechanics for the subjects that you are interested in. During the lectures, you might have a feeling why statistical mechanics could have a broad range of applications. If you are interested in X, you can try to google “statistical mechanics and X.” I believe you can find something interesting.
♠ The bottom line is: DO NOT LEARN SUBJECTS BY ATTENDING LECTURES ONLY. You can become better and better by thinking independently, but not by attending more and more lectures
How to benefit from the course?
| The correct mindset: to pass the course is not difficult; to learn something requires hard work ! | |
| ♠ | For students who want to work in theoretical physics: The bar for theoretical physics is high. It would help if you tried to learn statistical |
| mechanics by self-studying the subject. Try to self-studying the two textbooks and discuss with classmates, TAs, and me during office hours for those important conceptual questions. | |
| ♠ | The bar is also high for students who want to work in experimental physics: Try to connect statistical mechanics with experimental phenomena |
| that you have learned. I will mention some examples. However, those examples are far from enough to build the physics intuition for an outstanding experimentalist. | |
| ♠ | For students who do not belong to above-mentioned categories: The bar is even higher. Try to find out the possible use of statistical mechanics |
| for the subjects that you are interested in. During the lectures, you might have a feeling why statistical mechanics could have a broad range of applications. If you are interested in X, you can try to google “statistical mechanics and X.” I believe you can find something interesting. | |
| ♠ | The bottom line is: DO NOT LEARN SUBJECTS BY ATTENDING LECTURES ONLY. You can become better and better by thinking |
| independently, but not by attending more and more lectures | |
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完成版課程資訊〡
