Physics 561, Statistical Mechanics, Fall 2004, Section 19428

Summary:

This course will give you a general background in advanced statistical mechanics, which is the basic tool of physics linking microscopic features of particles (e.g. position and momentum of atoms or molecules) to macroscopic properties of materials (e.g. pressure and temperature).  This course is at a higher level than the typical problems found on the preliminary exam, and will not have a strong focus on thermodynamics in the way that Physics 461 and the preliminary exam  do.  Instead, Physics 561 will aim more at teaching you some of the techniques used to treat statistical mechanics of strongly interacting particles, including phase transitions.

Note that Physics 561 is a required course for the Ph.D. in Physics.

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Outline:

I. Review of basic statistical mechanics: harmonic oscillator, Bose and Fermi gases

II. Interacting classical gas

III. Basic phenomenology of phase transitions, Ising model, exact solutions, mean-field theory

IV. Thermal shape fluctuations of polymers and membranes

Textbook:

There is no required textbook for this course.  Course notes will be published on the web and will play the role of a textbook. However, you might want to consult some of the textbooks listed below.

Other books:

`Statistical Mechanics', by L.D. Landau and E.M. Lifshitz (Pergamon) - a really good book, with many of the classical topics that we will discuss beautifully presented.  E ven the old edition (one volume) is good.  Newer edition is split into two volumes; the second volume is not needed for this course.

`Equilibrium Statistical Physics', 2nd edition, by M. Plischke and B. Bergersen (World Scientific, 1994) - has most of the topics of this course and is up-to-date, including introductions to polymer and membrane fluctuations.  It is available in paperback at a relatively low price (< $50).

`Statistical Mechanics' by R.K. Pathria (Butterworth-Heinemann) - an excellent general text for the first 2/3 of the course.  This book is now a bit dated, but is still an excellent introduction.

`Statistical Mechanics' by S.K. Ma (World Scientific 1985) - another excellent text but not as encyclopaedic as Pathria.  This book is particularly good to read after you understand the basic methods of calculation of statistical mechanics.

`Theory of the Brownian Movement' by A. Einstein (Dover) - Really nice to read, and cheap, too. For the last part of the course.

Elementary Statistical Mechanics (at the Physics 461 level):

`Thermal Physics', Second Edition, by C. Kittel and H. Kroemer (Freeman and Co, New York 1984). 
Kittel and Kroemer may be purchased from barnesandnoble.com

Elementary Texts on Thermodynamics (also at the Physics 461 level, but good for review):

`Thermal Physics' by M. Sprackling (AIP Press, New York 1991).

`Heat and Thermodynamics' by M.W. Zemansky and R.H. Dittman (McGraw Hill).

These books may be ordered from either amazon.com or barnesandnoble.com. 

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Lecture Notes, and Other Downloadable Course Documents:

Problem Set 1 - Due Thursday September 9 2004 .pdf Solutions

Problem Set 2 - Due Thursday September 30 2004 (could be handed in the next Monday if you like) .pdf Solutions

Problem Set 3 - Due Thursday October 21 2004 .pdf Solutions

Problem Set 4 - Due Monday November 15 2004 .pdf Solutions

Problem Set 5 - Due Friday December 3 2004 .pdf Solutions

Final Exam .pdf Solutions

Hand-Written Lecture Notes  directory with .pdf files

These notes, used in Fall 2003, will be the basis for the new typeset notes above. You can read these scans of my handwritten lecture notes if you want to look ahead of the typeset stuff.

PDF files may be viewed and printed on PCs using the free program Acroread from Adobe.

Exams and Grading:

15% Midterm           October 19 2004, in class  
25% Final                 December
60% Homework      Approximately 6 problem sets, due roughly every two weeks, 4 problems per set, sets equally weighted

The grading is set up so that the homework is required in order to pass the course.  So do it!

Incompletes will be assigned only for students with documented medical problems that make finishing the course impossible.

For exams you may bring 3 pages (8.5 x 11 inches, both sides if you like) of your own handwritten notes.  No other materials can be used.  Calculators or pocket computers are not permitted.

Some Statistical Mechanics Web Pages

Ludwig Boltzmann

More Boltzmann

Quantum Gases - Fermi and Bose

Bose Condensation

Fermi Surface Database

Maria Goeppert Mayer

Joseph Edward Mayer

Interactive simulation of d=2 (32x32 spin) Ising model with h=0 (nifty! but note that Internet Exploder no longer supports Java as shipped, you need to add it yourself, or else use Mozilla, Netscape, or an old version of IE)

A nice list of Ising model web resources, oriented towards simulations

Brownian motion overview from Physics 450