| Instructor: |
Olexei Motrunich
Office: Sloan Annex 127 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: Sloan Annex 121 Email: hsinhua Office hours: Wed 4:00-5:00 |
| Textbook: |
M. Kardar, "Statistical Physics of Particles".
New York, NY: Cambridge University Press, 2007. ISBN 9780521873420
|
| Other texts: |
K. Huang, "Statistical Mechanics". R. K. Pathria, "Statistical Mechanics" L. D. Landau and E. M. Lifshitz, "Statistical Physics. Part 1". |
| 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 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
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.
Required reading: Chapter 1 of Kardar. |
|---|---|
| Lecture 2: | 1st Law. Heat engines. 2nd Law of Thermodynamics.
Thermodynamic temperature scale.
Required reading: Chapter 1 of Kardar. Solved Problem 1.3 in Kardar. Cool (or hot) outside reading: Heat engines. |
| Lecture 3: | 2nd Law of Thermodynamics and notion of entropy.
Applications of the 1st and 2nd law
Required reading: Chapter 1 of Kardar. Some lecture notes: Applications of the 1st and 2nd laws of thermodynamics |
| Lecture 4: | Applications of the 1st and 2nd law.
Thermodynamic stability.
Legendre transformations and 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 |
| Lecture 5: | Thermodynamic potentials and their physical applications.
Required reading: Chapter 1 of Kardar. Lecture notes for Lecture 4. Suggested reading: Application to liquid-gas transition (not covered in class). Chapter 2 of Huang. |
| Lecture 6: | 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 7: | Finish simple probability example. Microcanonical ensemble.
Justification of the equal probability postulate. Liouville's
theorem.
Reading: Same as lecture 6. First section of Chapter 3 in Kardar. Lecture 3 of Mike Cross' lectures. |
| Lecture 8: | Microcanonical ensemble. Justification of the entropy definition.
Temperature, chemical potential, pressure.
Required reading: Chapter 4 in Kardar. Lecture 4 of Mike Cross' lectures. |
| Lecture 9: | Examples of microcanonical ensemble.
Required reading: Chapter 4 in Kardar. Lecture 4 of Mike Cross' lectures. History reading: The Sackur-Tetrode Equation: How Entropy Met Quantum Mechanics |
| Lecture 10: | Canonical ensemble.
Required reading: Chapter 4 in Kardar. Lectures 6,7 of Mike Cross' lectures. |
| Lecture 11: | Examples of the canonical ensemble. Grand-canonical ensemble.
Required reading: Chapter 4 in Kardar. Suggested reading: Lectures 7-9 of Mike Cross' lectures. |
| Lecture 12: | Wrap-up grand-canonical ensemble.
Towards quantum Stat Mech -- Polyatomic gases.
Required reading: Chapter 6 in Kardar or Lectures 9-10 of Mike Cross' lectures. Suggested reading: Lectures 18-19 of Mike Cross' lectures. |
| Lecture 13: | Polyatomic gases; vibrational and rotational degrees of freedom.
Specific heat of solids.
Required reading: Chapter 6 in Kardar or Lecture 16 of Mike Cross' lectures. |
| Lecture 14: | Sound modes in solids and Debye calculation of specific heat.
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.
Required reading: Same as Lecture 14 |
| Lecture 16: | Ideal quantum gases. Many-particle states of bosons and fermions.
Calculations in the grand canonical ensemble. Fermi-Dirac and
Bose-Einstein distribution.
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.
Required reading: Chapter 7 in Kardar. Suggested reading: Mike Cross's lectures 13, 17. |
| Lecture 18: | Sommerfeld expansion for degenerate electron gas.
Specific heat of electron gas. Specific heat of solids.
Begin Bose gas at low T and Bose-Einstein Condensation.
Required reading: Chapter 7 in Kardar. 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). Reading 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: | Bose-Einstein Condensation. Superfluid He4
Required reading: Chapter 7 in Kardar. Lecture notes: Bose Einstein Condensation ; Superfluid He4 |