Phys 935: Statistical Mechanics                                                                                                                                                                                    
 
Spring 2006
T TH 9:40-11:00,   DEM 304

Instructor:   Silas Beane

Office:    DEM 209E                   Phone:   603-862-2720

email:   silas at physics.unh.edu      web:   http://www.physics.unh.edu/~silas                                                                                                                                                                       
Office hours:   to be determined



Course information

Purpose

This course offers an introduction to statistical mechanics at the graduate level. Basic knowledge of thermal physics is assumed.
The first two weeks will review basic thermodynamic concepts. The bulk of the course will be dedicated to developing the
relationship between thermodynamics and statistical mechanics for classical and quantum systems in equilibrium. If time
allows, some special topics of current interest will be covered.

Textbook

The main textbook for this course is:  Statistical Mechanics by R.K. Pathria                                         

Email and Office Hours

I strongly encourage students to communicate with me by email for bureaucratic issues. At times, I'll communicate with the class by email.
Please, no physics questions via email!

If necessary, you may visit me outside of office hours but please do not be offended if I'm unable to speak with you immediately.

Homeworks, Exams and Grades

The grades for this course will be based on homework (60%), a take-home midterm exam (20%) and a take-home final exam  (20%). The final exam will be comprehensive.

You will have two weeks to complete each homework set; there will be six homework assignments.  The homeworks will be long and difficult. If you start working on an assignment
the day before it's due, you will not finish it in time. Late homeworks will not be accepted unless there is a compelling rationale.

I encourage you to work on the homework in groups. However, you must list your collaborators on your manuscript.
There is no collaboration permitted on the exams.

I believe that most of what you'll get out of this class will be from the homeworks. Due to the large amount of material that must be covered, generally I will present the theoretical
formalism and the worked problems will be left to the homework.


Some useful texts (on reserve in the library)
 
L.D. Landau and E.M. Lifschitz, Statistical Mechanics (part I)

K. Huang, Statistical Mechanics

L.E. Reichl , Statistical Physics

D.L. Goodstein , States of Matter

R. Feynman: The Feynman Lectures on Physics


Calendar  (topics covered & homework)


         Week


1:   1/17,1/19
Introduction
Thermodynamic variables
Laws of thermodynamics
 Homework 1 (ps,pdf)(Due 2/2)
2:  1/24, 1/26
Thermodynamic potentials
Thermodynamic derivatives
Magnetic variables

3:   1/31, 2/2
Elementary probability theory
Liouville's theorem
Microcanonical ensemble
Homework 2 (ps,pdf)(Due 2/16)
4:    2/7,2/9
Microcanonical ensemble (cont.)
Statistical basis of thermodynamics: the ideal gas
Gibb's paradox and entropy of mixing

5:   2/14, 2/16
Canonical ensemble
Applications of the canonical ensemble: the ideal gas
Connection between canonical and microcanonical ensembles
Homework 3 (ps,pdf)(Due 3/2)
6:   2/21, 2/23 Applications of the canonical ensemble: harmonic oscillators
Applications of the canonical ensemble: magnetic dipoles

7:    2/28, 3/2 Applications of the canonical ensemble: magnetic dipoles (cont)
Negative temperatures
The grand canonical ensemble
Midterm Exam  (ps,pdf)(Due 3/9)
 8:    3/7, 3/9
The grand canonical ensemble (cont)     (Tuesday class replaced with office hour)

     3/14, 3/16
Spring Break

9:  3/21, 3/23
The grand canonical ensemble (cont)
Quantum statistical mechanics: the density matrix
Quantum statistical mechanics: the ensembles
Homework 4 (ps,pdf)(Due 4/6)
10:   3/28, 3/30
Systems of indistinguishable particles
Density matrix of free particles

11:    4/4, 4/6
Quantum ideal gas in canonical ensemble
Occupation numbers
(4/6 Silas at Fermilab)
Homework 5 (ps,pdf)(Due 4/20)
12:  4/11, 4/13
Ideal Bose systems
Bose-Einstein condensation
(4/11 missed)

13:  4/18,               4/20,4/21
Blackbody radiation
Ideal Fermi systems
Thermodynamics of ideal Fermi systems
Homework 6 (ps,pdf)(Due 5/4)
 
14:   4/25, 4/27
Electron gas in Metals
Magnetic properties of ideal Fermi systems
Introduction to the Ising model

        
15:  5/2,  5/4

Ising model and binary alloys
General formulation
1-d Ising model
Mean field theory and spontaneous magnetization

Final Exam
(ps,pdf)(Due 5/11)

The outline above is subject to radical change as the semester progresses.