Physics 505 -- Statistical Mechanics
Spring 2014

Meeting Time: TR 11:00-12:15 in PandA 184

Instructor: Dr. V. M. Kenkre
Email: kenkre@unm.edu
Office: PandA 35
Office Hours: None scheduled, but available by appointment (Catch him if you can! ...in his office or PandA 22.)

Teaching Assistant: Anastasia Ierides
Email: aierides@unm.edu
Office: PandA 22
Office Hours: TR 12:30-13:30; also available by appointment

Course Outline

Roughly speaking there are three main topics that will be covered in this course:

1. Equilibrium Statistical Mechanics (the evaluation of partition functions, the use of the Boltzmann factors for classical as well as quantum systems, etc.) This will constitute about one third or less of the semester.
2. Stochastic Aspects of Statistical Mechanics (introduction of probabilities, systems of huge degrees of freedom, etc.)
3. Non-Equilibrium Statistical Mechanics (time-dependent phenomena, philosophical questions associated with the subject, etc.)

Grading

Your grade in this course will be decided by your performance without reference to that of the rest of the class. (Do your best!)

The credit distribution is as follows:

• 60% -- Three midterm exams will be given at the end of or around the end of the months of February, March, and April. These exams may be in class closed-book with one 8.5 x 11 sheet of notes or take home. Note, however, that if the exams are take-home they would need to be typeset in PDF format if emailed or printed hardcopy depending on how they will be turned in. Depending on the performance of the class the lowest test grade MAY be dropped as the other two will each count for 30% of your grade. (As it is, no final is scheduled.)
• 25% -- Homeworks, consisting of 2-4 problems a week, typically emailed out to the class by Dr. Kenkre, or by the TA, to be handed in one week from the day they are given at class time.
• 15% -- (Freebie!) Lecture notes for each week must be typed up. These should be submitted electronically in PDF format to aierides@unm.edu every week before 5 PM on Monday. LaTeX is strongly recommended, but not required.

Homeworks

• Homework #1 -- Solution
• Homework #2 -- Solution
• Homework #3 -- Solution
• Homework #4 -- Solution
• Homework #5 -- Solution
• Homework #6 -- Solution
• Homework #7 -- Solution

Midterm Exams

• Midterm Exam #1 -- Solution
• Midterm 2 will be sent via e-mail, on the evening of Thursday, April 17th, and will be due on the evening of Saturday, April 19th, typed up, in PDF format.

Class Notes

Papers, Notes, Books and Other Resources

Papers and other notes:

• E. Montrol and K. Shuler, The Relaxation of a System of Harmonic Oscillators
• V. M. Kenkre, Master-equation theory of the effect of vibrational relaxation on intermolecular transfer of electronic excitation
• The Bogoliubov-Born-Green-Kirkwood-Yvon Hierarchy
• Kinetic Theory
• Generalized-master-equation theory of excitation transfer - Kenkre and Knox
• The Generalized Master Equation and Its Applications - Kenkre
• A Theorem On The Single Particle Energy In A Fermi Gas With Interaction - Van Hove
• Energy Corrections and Persistent Perturbation Effects in Continuous Spectra - Van Hove
• The Approach to Equilibrium in Quantum Statistics - Van Hove
• The Ergodic Behaviour of Quantum Many-Body Systems - Van Hove
• On the Identity of Three Generalized Master Equations - Zwanzig

• Kathrin's Notes on Numerical Laplace Inversion
• J. Abate and W. Whitt, A Unified Framework for Numerically Inverting Laplace Transforms

Excerpts from Books

• Statistical Mechanics - Pathria
• Kinetic Theory of Gases - McQuarrie
• The reading material for Homework 5 The Boltzmann Equation - McQuarrie
• Lectures on The Statistical Mechanics of Irreversibility - Zwanzig, Excertpt from "Quantum Statistical Mechanics" - P.H.E. Meijer
• Statistical Mechanics of Irreversibility- Zwanzig, Excerpt from "Lectures in Theoretical Physics" Volume III - Edited by Wesley E. Brittin, B.W. Downs, and Joanne Downs

Books

• A Modern Course in Statistical Mechanics -- Linda Reichl, QC174.8 R44
• Equilibrium and Non-Equilibrium Statistical Mechanics -- Radu Balescu, QC174.8 B34 1975

• Statistical Physics -- Wannier
• Statistical Mechanics -- Pathria
• Statistical Mechanics, Kinetic Theory, and Stochastic Processes -- Heer
• An Introduction to Statistical Mechanics -- Phillippe Dennery
• Elements of Statistical Mechanics -- D ter Haar
• The Principles of Statistical Mechanics -- Tolman
• Statistical Mechanics -- Huang
• Nonequilibrium Stat Mech by Zwanzig, Oxford 2001
• The Langevin Equation by Coffey et al, World, 2003
• The Fokker-Planck Equation by Risken, Springer
• Stoch Proc in Phys and Chem by van Kampen
• Selected Papers in Noise, ed. Wax, Dover
• Foundation of Stat Mech Series, North-Holland
• Stat Mech and Stat Methods ed. Landman, Plenum
• Statistical Phys I and II by Kubo et al., Springer
• Exciton Dynamics in Molecular Crystals and Aggregates by Kenkre and Reineker
• Modern Challenges in Stat Mech, ed. Kenkre and Lindenberg

Software Tools:

• Texmaker -- A free cross-platform LaTeX editor for linux, macosx and windows systems that integrates many tools needed to develop documents with LaTeX. In order for this to configure properly, a LaTeX distribution such as MiKTEX has to also be installed.
• gnuplot -- A very powerful free plotting program.
• GNU Octave -- A free language for numerical computations. Octave is very similar to MATLAB.
• You can run Mathematica, Maple, or MATLAB from UNM's servers. For instructions, see this page. Windows users will need to install an SSH client (such as PuTTY).