| Instructor: |
Olexei Motrunich
Office: West Bridge 165C Phone: (626) 395-8894 Email: motrunch |
|---|---|
| Class Meets: | Tue, Th 9:00 - 10:30, Downs 107 |
| Office Hours: | Tue 5:00-6:00
|
| Teaching Assistant: | Hsin-Hua Lai
Office: West Bridge 155 Email: hsinhua Office hours: Wed 2:00-3:00 |
| Textbook: |
M. Kardar, "Statistical Physics of Particles".
New York, NY: Cambridge University Press, 2007. ISBN 9780521873420
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| Other texts: |
K. Huang, "Statistical Mechanics"; R. K. Pathria, "Statistical Mechanics"; L. D. Landau and E. M. Lifshitz, "Statistical Physics. Part 1"; K. Huang, "Introduction to Statistical Physics"; A. Sommerfeld, "Thermodynamics and Statistical Mechanics". |
| Homework and Grading: | There will be a weekly homework assignment anounced in class (and via email), due one week later. There will be a midterm exam and a final exam (both take-home). Grades will be based on the homework (40%), midterm (30%), and final exams (30%). |
| Course Policies: | We will adhere to standard course policies such as Mike Cross' Ph106a course policies . Note in particular late homeworks and extensions policy: No grade if submitted later than one week after the due date; 50% grade for any late homeworks up to one week late; one "free" (full-credit) late homework up to one week late (indicate on the title page page that this is the "free" late homework). |
Course Description:
This term covers the basic principles of statistical mechanics,
applications to simple systems that can be solved exactly,
and the connections with thermodynamics.
Topics include: review of the basic ideas of thermodynamics
(the concepts of temperature, work, heat, and entropy);
postulates of classical statistical mechanics,
microcanonical, canonical, and grand canonical ensembles;
polyatomic gases, lattice vibrations, and photon gas;
quantum statistical mechanics;
Fermi and Bose systems (electrons in metal, Bose-Einstein condensation,
and superfluids).
Topics from modern statistical mechanics including phase transitions
and broken symmetries, classical field theories, and renormalization
approach to collective phenomena will be covered in the next two terms
(Phy127b,c).
Prerequisites:
Phy 12c; some knowledge of thermal physics, classical mechanics, and
quantum mechanics
Working course plan:
Phy127a 2009 course plan
Links to Statstical Physics courses on the web
Mike Cross' Phy127a 2005 lectures
Mehran Kardar's MIT lectures
LECTURES:
| Lecture 1: | Review of Thermodynamics. Notions of temperature and heat.
1st Law of thermodynamics.
Required reading: Chapter 1 of Kardar. |
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| Lecture 2: | 1st Law. Heat engines. 2nd Law of Thermodynamics.
Thermodynamic temperature scale. Entropy.
Required reading: Chapter 1 of Kardar. Solved Problem 1.3 in Kardar. Cool (or hot) outside reading: Heat engines. Fun reading: Sustainable Energy --- without the Hot Air (article from E&S Summer 2010 issue ) |
| Lecture 3: | Applications of the 1st and 2nd laws.
Required reading: Chapter 1 of Kardar. Some lecture notes: Applications of the 1st and 2nd laws of thermodynamics |
| Lecture 4: | Thermodynamic stability.
Legendre transformations and thermodynamic potentials.
Significance of thermodynamic potentials.
Required reading: Chapter 1 of Kardar. Some lecture notes: Thermodynamic stability, Legendre transformations and thermodynamic potentials. See also Lecture 10 and handout on thermodynamic potentials from Mike Cross' lectures Suggested reading: Application to liquid-gas transition (not covered in class). Chapter 2 of Huang. |
| Lecture 5: | Equilibrium statistical mechanics - overview of ensembles.
Simple probability example.
Suggested reading: Chapter 2 of Kardar. Required reading: Lecture 1 and 2 of Mike Cross' lectures |
| Lecture 6: | Finish simple probability example. Microcanonical ensemble.
Justification of the equal probability postulate. Liouville's
theorem.
Reading: Same as lecture 5. First section of Chapter 3 in Kardar. Lecture 3 of Mike Cross' lectures. |
| Lecture 7: | Finish Liouville's theorem. Microcanonical ensemble. Justification
of the entropy definition. Temperature, chemical potential, pressure.
Start two-level systems.
Required reading: Chapter 4 in Kardar. Lecture 4 of Mike Cross' lectures. |
| Lecture 8: | Examples of microcanonical ensemble: two-level systems; idal gas;
entropy of mixing.
Required reading: Chapter 4 in Kardar. Lecture 4 of Mike Cross' lectures. History reading: The Sackur-Tetrode Equation: How Entropy Met Quantum Mechanics |
| Lecture 9: | Canonical ensemble. Two-level system example.
Required reading: Chapter 4 in Kardar. Lectures 6,7 of Mike Cross' lectures. |
| Lecture 10: | Examples of the canonical ensemble: ideal gas and equipartition
theorem. Grand-canonical ensemble.
Required reading: Chapter 4 in Kardar. Suggested reading: Lectures 7-9 of Mike Cross' lectures. |
| Lecture 11: | Connection between thermodynamics and information theory:
Entropy and missing information; Equlibrium and maximal entropy approach;
Information-theoretic derivation of ensembles.
Lecture notes: Thermodynamics and Information theory. Suggested reading: Entropy as Ignorance Chapter 5.3 in book Entropy, Order Parameters, Complexity (from web page of James Sethna); article by Jaynes Evolution of Carnot's principle on relation between thermodynamics and maximal entropy approaches; Lecture 11 of Mike Cross' lectures and references there. |
| Lecture 12: | More examples of canonical ensemble and moving towards quantum
Stat Mech: Polyatomic gases; vibrational and rotational degrees of
freedom.
Required reading: Chapter 6 in Kardar Suggested reading: Lectures 18-19 of Mike Cross' lectures |
| Lecture 13: | Polyatomic gases; vibrational and rotational degrees of freedom.
Specific heat of solids. Sound modes in solids: 1d example.
Required reading: Chapter 6 in Kardar or Lecture 16 of Mike Cross' lectures. |
| Lecture 14: | Debye calculation of specific heat of solids.
Quantum Statistical Mechanics. Density matrix
Required reading: Chapter 6 in Kardar. Chapter 3.4 in J.J. Sakurai, Modern Quantum Mechanics. Suggested reading: Mike Cross's lecture 12 introduces the density matrix somewhat differently by tracing out the environment, but all calculations with it are the same as in the ensemble definition. |
| Lecture 15: | Density matrix and quantum stat mech. Begin ideal quantum gases;
many-particle states of bosons and fermions.
Required reading: Same as Lecture 14. Chapter 7 in Kardar |
| Lecture 16: | Ideal quantum gases: Calculations in the grand canonical ensemble.
Fermi-Dirac and Bose-Einstein distribution. Case of 3D gases with
quadratic dispersion
Required reading: Chapter 7 in Kardar. Suggested reading: Mike Cross's lecture 13. |
| Lecture 17: |
Ideal quantum gases - case of 3d and quadratic dispersion.
Analysis at high temperature -- classical limit and first quantum
correction.
Behavior at low temperature. Fermi gas at zero temperature.
Sommerfeld expansion for degenerate electron gas.
Required reading: Chapter 7 in Kardar. Mike Cros' lecture 17. Lecture notes: Degenerate Fermi gas . Suggested reading: Mike Cross's lectures 13 - 17; Very good account of the Sommerfeld theory of metals can be found in Ch.1-2 of N. W. Ashcroft and N. D. Mermin, "Solid State Physics"; Historical reading: Arnold Sommerfeld More historical reading: The Development of the Quantum Mechanical Electron Theory of Metals: 1900-28 This is just one of the wonderful collection of historical articles on The Beginnings of Solid State Physics , Proceedings of the Royal Society of London, A, Vol. 371, No. 1744 (1980). |
| Lecture 18: | Finish Sommerfeld expansion for degenerate electron gas;
specific heat of electron gas; specific heat of solids.
Bose gas at low T and Bose-Einstein Condensation.
Required reading: Chapter 7 in Kardar. Mike Cross' lecture 14. Lecture notes: Bose Einstein Condensation More readings about BEC: wiki page with tons of references, e.g. pop introduction to BEC ; 2001 Nobel Prize in Physics with nice Nobel lectures by each of the three recipients: Eric Cornell , Wolfgang Ketterle , and Carl E. Wieman . |
| Lecture 19: | Wrap up BEC. Superfluid He4.
Required reading: Chapter 7 in Kardar. Mike Cross' lecture 15. Lecture notes: Superfluid He4 |