Physics 561, Fall 2000, Statistical Mechanics, Section 90954

Course 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 all graduate students.

---

Course 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,and mean-field theory of Ising model

IV. Exact solution of the Ising model in one and two dimensions

V. Landau theory, dimensionality, renormalization group, universality

VI. Thermal shape fluctuations of polymers and membranes

VII. Dynamics of thermal fluctuations: detailed balance,Langevin equation for harmonic oscillator, diffusion

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.

Books at the Level of 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.  The discussion of renormalization group will be pretty similar to what you can read in this book.  Also, 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 old, 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.

`Modern Theory of Critical Phenomena' by S.K. Ma (1976) - excellent introduction to the phase transition and renormalization group parts of the course.  However, it will be useless for the early part of the course.

`The Theory of Critical Phenomena: An Introduction to the Renormalization Group' by J.J. Binney et al (Oxford Science) - like Ma, a good introduction to the critical phenomena part of the course, and like Ma, largely useless for the first part of the course.

`Theory of the Brownian Movement' by A. Einstein (Dover) - relevant to the last part of the course, and really nice to read.

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. 

---

Lecture Notes, Problem Sets and Other Downloadable Course Documents:

Lecture Notes from Fall 1999 Physics 461 ( one big .pdf file (75 pages, about 13 Mb))

In-class Quiz 1  August 21 2000  (HTMLPDFPS)

Problem Set 1 due Wednesday September 6 2000  (HTML PDFPS solutions)

Problem Set 2 due Monday September 25 2000  (HTML PDFPS  solutions)

Problem Set 3 due Friday October 13 2000  (HTMLPDFPS solutions)

Midterm Exam Wednesday October 18 2000  (HTMLPDFPS solutions)

Problem Set 4 due Friday November 3 2000  (HTMLPDFPS solutions)

Problem Set 5 due Monday November 20 2000  (HTMLPDFPSsolutions)

Problem Set 6 - for review, not for credit   (HTML PDF PS solutions)

A recent article in Nature about critical phenomena in ferromagnets (!)  A recent article in Nature about critical phenomena in ferromagnets (!)  http://www.nature.com/nlink/v408/n6810/abs/408337a0_fs.html

PS files can be viewed and printed on most PCs, Macs and other workstations.

PDF files may be viewed and printed on almost any PC with the free program Acroread from Adobe.

Most documents will be posted in HTML format, created with a program called tth. To view this file, you need Netscape 4.x.   On Windows machines all should work well.   On unix machines you must add a line to the file .Xdefaults in your home directory (or if the file is absent, just make one with one line):

Netscape*documentFonts.charset*adobe-fontspecific: iso-8859-1

Exams and Grading:

15% Midterm           October 
25% Final                 December
60% Homework      Approximately 7 problem sets due every two weeks, 4 problems per set, sets equally weighted

Note that the grading is set up so that the homework is required in order to pass the course.  Don't come to me in the last week of the course and ask that you be excused from doing the homework.

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

For exams you may bring 3 pages of your own handwritten notes.  No other materials can be used.  Calculators are really not needed.