Physics 847 (Spring, 2010)

[Introduction and General Format|Syllabus]
[Problem Sets| Suggested Reading]
[Offices Hours; Grader| [Lecture Notes| Random Information]


Introduction and General Format

Physics 847 is the second quarter of a two-quarter graduate sequence on statistical physics. The text will continue to be "Statistical Physics," 2nd edition, by R. K. Pathria (Butterworth-Heinemann, Oxford, UK and Woburn Ma, 1996); ISBN 0 7506 2469 8; list price $94.95, currently available on amazon.com for $71.21 or less). However, I often will not follow this text very closely.

The instructor is David Stroud. The grader is Ranjan Laha (room PRB3031, tel. 614-247-8463, email laha.1@pacific.mps.ohio-state.edu).

We will meet in McPherson Lab 2017, on Tuesdays and Thursdays from 9:30 to 10:18 and 10:30 to 11:18.

Grades will be based on one midterm (about 25%), a final (about 40%), and homework (about 35%). In grading the homework, I will discard your lowest set and obtain a percentage score from the remaining sets. (Note: this is a different policy from last quarter.)

The midterm will take place on Tuesday, May 4 from 9:55 to 11:18. The final will be given on Thursday, June 10 from 9:30 to 11:18.

Besides the principal textbook, I may occasionally take some material from various other books. Some other leading books on the subject of statistical physics are the following. I hope to add more to this list shortly:

``Statistical Mechanics,'' by Kerson Huang (1987). Originally written in the 1960's, very good on such topics as the Ising model and liquid helium. Quite readable.

``Thermal Physics,'' by Charles Kittel and Herbert Kroemer (1980). Written as an advanced undergrad textbook, but has all the basics of statistical physics and many applications in condensed matter physics.

``Statistical Physics of Particles,'' by Mehran Kardar (2007). A rather original presentation of statistical physics, with lots of applications. Last year's text.

``Statistical Physics of Fields,'' by Mehran Kardar (2007). This is a more advanced text, developed from the lectures of a leading researcher in the field. An extremely clear description of such topics as fluctuation phenomena, renormalization and scaling theory, stochastic dynamics, etc.

``A Modern Course in Statistical Physics,'' by L. E. Reichl. Includes both thermodynamics and statistical mechanics. Used as a text in this course a couple of years ago.

``Introduction to Modern Statistical Mechanics,'' by David Chandler. A text by a leading practitioner in the area of chemical physics. This book includes a compact but lucid discussion of the standard material, and also has chapters on numerical techniques such as Monte Carlo methods. See also the companion solution manual.

``Statistical Mechanics: A Set of Lectures,'' by Richard P. Feynman (paperback edition, 1998). Somewhat advanced if you haven't had much previous exposure to statistical physics, but full of original insights, new methods, and important applications.

``Statistical Mechanics, 2nd Edition'' by R. Kubo, H. Ichimaru, T. Usui, N. Hashitsume (North-Holland, 1988). Old but a clear and readable introduction, with a large number of solved examples and problems.

``Statistical Physics, Third Edition, Part 1'' by L. D. Landau and E. M. Lifshitz. A famous text, somewhat updated here.

``Statistical Physics, Part 2,'' by E. M. Lifshitz and L. P. Pitaevskii. More advanced material, such as normal Fermi liquid, Green's functions for Fermi systems, and other problems in many body physics.

``Lectures on Phase Transitions and the Renormalization Group,'' by Nigel Goldenfeld (1992). A clear and quite detailed exposition of this important topic. May be useful for part of the second quarter of this sequence.

Syllabus

The syllabus will be similar to that described in the course catalog. More details will be announced very shortly.

Note: a good online math reference is http://mathworld.wolfram.com, which has lots of analysis, plus a great deal of information about special functions. Two good books are "Tables of Integrals, Series, and Products," 6th ed., by Gradshteyn, Ryzhik, Jeffrey, and Zwillinger (Academic, San Diego, 2000), and "Mathematical Methods for Physicists," by Arfken, Weber, and Weber (Academic, San Diego, 2001).

Problem Sets

I plan to have weekly problem sets, mostly due on Thursdays. If possible, turn in the problem sets into the mailbox of the grader, Ranjan Laha, in PRB. Alternately, you may turn them into my mailbox, turn them in during class, hand them to me in my office, or or slip them under my office door (2048PRB) if I am not there.

In calculating the homework grade, I will sum up the homework scores, discard the lowest score, and convert the sum to a percent. Note: this is a change from last quarter's policy.

In general, I do not object if you discuss the problems with one another while working on them. However, you should write up your solutions independently.

oProblem Set 1.

oSolutions to Problem Set 1.

oProblem Set 2.

oSolutions to Problem Set 2.

oProblem Set 3.

oSolutions to Problem Set 3.

oProblem Set 4.

oSolutions to all of PS4 except problem 2.

oSolution to problem 2 of PS4.

oProblem Set 5.

oSolutions to PS5.

oProblem Set 6.

oSolutions to PS6.

oProblem Set 7.

oSolutions to PS7.

oProblem Set 8.

oSolutions to PS8.

Office Hours; Grader

My office is Room 2048 of the Physics Research Building. My office telephone no. is 292-8140 and my email address is stroud@mps.ohio-state.edu. My office hours will be Tu 11:30 - 12:30 and Th 1 - 2. You can also see me by appointment, or you can simply drop by, and I am generally happy to talk to you if I do not have another visitor. Please consult the grader, Ranjan Laha, if you have any questions about the homework grading.

Lecture Notes

I expect to post my (hand-written) lecture notes as I complete them. They are posted as a study aid but they are not guaranteed to be error-free.

oLectures of March 30 and April 1 (introduction; density matrix and its equation of motion; free fermions and bosons in the grand canonical ensemble.

oLectures of April 6 and part of April 8 (connection between classical and quantum-mechanical partition functions for 1D harmonic oscillator and 3D interacting particles; start of ideal Bose gas. Note: three omitted pages are related to assigned homework problem.

oRemainder of April 8 and lecture of April 13 (remainder of ideal Bose gas; application to blackbody radiation and to Debye model of specific heat of a solid).

o Fourth set of lecture notes: introduction to Fermi-Dirac statistics with application to free gas of spin-1/2 particles.

o Fifth set of lecture notes: more on Fermi-Dirac statistics (Sommerfeld expansion; Pauli paramagnetic susceptibility).

o Sixth set of lecture notes: Rough sketch of Landau diamagnetism in three and two dimensions (will probably not be covered in class); start of model for binding energy of metallic hydrogen.

o Seventh set of lecture notes: end of metallic hydrogen; model for white dwarf stars.

o Eighth set of lecture notes: Introduction to Ising model (definition, one version of mean-field theory).

o Ninth set of lecture notes: mean field theory for Ising model in a B-field; another version of mean-field theory.

o Tenth set of lecture notes: Ising model in 1D; exact solution via transfer matrix. Ising model applied to phase separation in binary alloys.

oEleventh set of lecture notes: Still more on Ising model and applications (rather cryptic).

oTwelfth set of lecture notes: Heisenberg model, spin waves.

oThirteenth set of lecture notes: non-ideal gases, configurational integral, equation of state including second virial coefficient.

oFourteenth set of lecture notes: more on non-ideal gases, including virial equation of state and another derivation of the second virial coefficient.

oFifteenth set of lecture notes: introduction to critical phenomena and phase transitions, Landau theory of phase transition, Van der Waals equation as a mean-field theory.

oSixteenth set of lecture notes: Scaling hypothesis; relations between critical exponents from scaling hypotheses.

oSeventeenth set of lecture notes: introduction to non-equilibrium statistical mechanics (almost all Boltzmann equation).

oFive minute primer on Monte Carlo methods in statistical physics.

Random Information

oJ. Willard Gibbs

o Nicolas Leonard Sadi Carnot

o Rudolf Julius Emmanuel Clausius

oJames Clerk Maxwell

oLudwig Boltzmann

oWalther Nernst

oSatyendra Nath Bose

oAlbert Einstein

o Max Planck

oEnrico Fermi

oPaul Adrien Marie Dirac

oKenneth G. Wilson