PHY831 - Graduate Statistical Mechanics: Fall 2012
Lectures MWF 11:30-12:20, BPS1308
Professor Phillip Duxbury: Office: BPS 4260, Email: duxbury at pa.msu.edu
Helproom - TBA
Office hours - email me for an appointment
Active lecture notes and problem sets.
Complete Lecture Notes and Problems for Part 4
Complete solutions to problems for Part 4
Helproom: Thursday Dec. 6, 7-8 pm BPS 1308
Midterm 4: Friday Dec. 7, usual time and place
Helproom: Wednesday Dec. 12, 11:30am - 12:30pm BPS 1308. All
of the homeworks, quizzes and midterms you handed in will be available.
Final and Subject Exam: Friday Dec. 14, 2-5pm, BPS 1400
Final covers Parts 1-3 and BCS theory at finite temperature in Part 4
Course schedule and outline
Part 1: (LL, PB) Foundations: (10 lectures)
History, Heat, Engines, Kinetic theory and Entropy.
Computational methods, molecular dynamics, ensembles, ergodicity.
Foundations of Equilibrium Statistical Mechanics.
Ensembles, Boltzmann factors, Quantum systems.
Computational methods, Monte Carlo and detailed balance.
Free energies and thermodynamics.
Fun with thermodynamic relations.
Fluctuations and response functions.
Monday September 10: Homework 1 is due and Quiz 1 (20 minutes) in class
Homework 1 - do problems 1-9, hand in problems 8,9. Quiz 1 covers quiz problems 1-8 and
homework problems 1-9.
Monday September 17: Homework 2 is due and Quiz 2 (20 minutes) in class
Homework 2 - do problems 10-16, hand in problems 15,16. Quiz 2 covers quiz problems 9-18 and
homework problems 10-16.
Monday September 24: Midterm I (50 minutes) in class
Complete Lecture Notes and Problems for Part I
Complete Problems and Solutions for Part I
Midterm I Exam and Solutions
Part 2: (H, PB, LL) Key solvable systems: (10 lectures)
Non-interacting spin systems.
Ideal Classical gas.
Classical harmonic oscillators.
Ideal Fermi gas, electron gas, white dwarf stars.
Ideal Bose gas, photons, phonons, bose condensation,
The early universe. Electrons and phonons in metals.
Solvable Ising systems. Magnetic properties of the electron
gas.
Friday October 5: Homework 3 is due and Quiz 3 (20 minutes) in class
Homework 3 - do problems 1-9, hand in problems 6, 8. Quiz 3 covers quiz problems 1-9 and
homework problems 1-9.
Monday October 15: Homework 4 is due and Quiz 4 (20 minutes) in class
Homework 4: hand in solutions to assigned problems 10,14
Quiz 4 covers quiz problems 9-18 and assigned problems 10-16
Monday October 22: Midterm II (50 minutes) in class
Complete Lecture Notes and Problems for Part 2
Complete Problems and Solutions for Part 2
Midterm 2 Exam and Solutions
Part 3: (H, PB) Interacting systems, phase transitions and critical phenomena (11 lectures)
Interacting spin systems, Ising model.
Interacting classical gas, cluster expansion, van der Waals gas, virial Expansion.
BCS model of superconductivity. Scaling theory, universality, Landau theory, Ginzburg-Landau model.
Monday November 5: Homework 5 is due and Midterm 2 - take 2 in class
Homework 5: hand in solutions to assigned problems 5, 6
Monday November 12: Homework 6 is due, Quiz 5 and Quiz 6 (20 minutes each) in class
Homework 6: hand in solutions to assigned problems 8, 9
Quiz 5 and Quiz 6 cover Lectures 1-7, Quiz problems 1-17 and Assigned problems 1-11
You will not be asked to prove the linked cluster theorem in these quizzes.
Monday November 19: Midterm 3 (50 minutes) in class
You will not be asked to prove the linked cluster theorem.
You will not be asked to reduce the BCS mean field Hamiltonian
to diagonal form using the Bogolubov-Valatin transformation.
Complete Lecture Notes and Problems for Part 3
Solutions to problems for Part 3
Midterm 3 Exam and Solutions
Part 4: (H, PB) Scaling and complex systems (7 lectures)
Landau theory of phase transitions and critical phenomena, scaling.
Equilibrium and non-equilibrium dynamics
Monday December 3: Homework 7 is due and Quiz 7 (20 minutes) in class
Friday December 7: Midterm 4 (50 minutes) in class
Final Exam: Friday December 14, 2pm - 5pm (BPS 1400)
Course assessment
Weekly or biweekly homeworks (10%). Hand in a copy of your work, not the original.
Late homeworks will not be accepted without a written explanation.
Quizzes (random, almost weekly) (20%). Your worst quiz will be dropped.
Midterms (40%). Final (30%).
Books and other resources
There is no graduate level Statistical Mechanics text that covers the above material
in a clean and pedagogical way.
Landau and Lifshitz, volume 1 and Pathria and Beale are best for Part 1,
Huang for Parts 2-4. Some parts of Part 4 are not in any of these texts.
In any case it is a good idea to work through at least two texts, and for
that I suggest PB and H. Hopefully everyone has worked through a significant fraction
of a book such as KK or LL in an undergraduate statistical mechanics course.
Recommended (PB): R.K. Pathria and P.D. Beale, Statistical Mechanics Third Edition 2011
Recommended (H): K. Huang, Statistical Mechanics, Second Edition 1987
Recommended (LL): Statistical Physics, L.D. Landau and E.M. Lifshitz
Recommended but lower level (KK) : Thermal Physics, C. Kittel and H. Kroemer
Problems and solutions: Statistical Mechanics, R. Kubo
Professor Scott Pratt has a PHY831 www site
that is a good resource for PHY831 problems, past subject exams and his lecture notes.
Professor Steven Teitel has a nice set
of notes and problems with solutions.
Materials from Fall 2011 Course
Part 1: (LL, PB) Foundations: (10 lectures)
History, Heat, Engines, Kinetic theory and Entropy.
Computational methods, molecular dynamics, ensembles, ergodicity.
Foundations of Equilibrium Statistical Mechanics.
Ensembles, Boltzmann factors, Quantum systems.
Computational methods, Monte Carlo and detailed balance.
Free energies and thermodynamics.
Fun with thermodynamic relations.
Fluctuations and response functions.
Equilibrium and Non-equilibrium Dynamics.
Complete lecture notes for Part 1
Solutions to quiz and assigned problems for Part 1
Midterm I and solutions
Part 2: (H, PB, LL) Key solvable systems: (10 lectures)
Non-interacting spin systems.
Ideal Classical gas.
Classical harmonic oscillators.
Ideal Fermi gas, electron gas, white dwarf stars.
Ideal Bose gas, photons, phonons, bose condensation,
The early universe. Electrons and phonons in metals.
Solvable Ising systems. Magnetic properties of the electron
gas.
Complete lecture notes for Part 2
Solutions to quiz and assigned problems for Part 2
Midterm II and solutions
Part 3: (H, PB) Interacting systems, phase transitions and critical phenomena (9 lectures)
Interacting spin systems, Ising model.
Interacting classical gas, cluster expansion, van der Waals gas, virial Expansion.
BCS model of superconductivity.
Complete lecture notes for Part 3
Solutions to quiz and assigned problems for Part 3
Midterm III and Solutions
Part 4: (H, PB) Scaling and complex systems (9 lectures)
Landau theory of phase transitions and critical phenomena, scaling. GL theory, RG.
Equilibrium and non-equilibrium dynamics
Complete Lectures Notes for Part 4
Solutions to quiz and assigned problems for Part 4
Midterm IV and solutions
Subject Exam and Solutions