Physics 505 -- Statistical Mechanics
Fall 2016

Meeting Time: Tuesdays and Thursdays 11:00 AM - 12:15 PM in PandA 5

Instructor: Professor. V. M. Kenkre
Email: kenkre@unm.edu
Office: PandA 35
Office Hours: Available by appointment

Teaching Assistant: Jeffrey Ngo
Email: jzngo@unm.edu
Office: PandA 38
Office Hours: Tuesday and Wednesday 12:30 - 1:30 PM; 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

The credit distribution is as follows:

• 25% -- Homeworks
• 50% -- Midterms: Three midterms over the semester, each weighted 25%. Two best are chosen out of three.
• 15% -- (Freebie!) Lecture notes for each week must be typed up. These should be submitted electronically in PDF format to jzngo@unm.edu by 12pm on Monday.
• Latest announcement from Professor Kenkre regarding grades: The distribution of work towards your grade announced at the beginning of the semester and posted on the course site will lead to a tentative grade for each of you as follows: 25% homework + 15% notes + 20% each of the 3 midterm tests = 100%. The tentative grade will be emailed to you on Monday Dec. 12th. If you elect to take the final, it will be used in place of your worst test (20%).

Homeworks

• Homework #1 Due Sept. 15, 2016 -- Solution
• Homework #2 Due Sept. 29, 2016 -- Solution
• Homework #3 Due Oct. 20, 2016
• Homework #4 Due Nov. 1, 2016 -- Solution
• Homework #5 Due Nov. 10, 2016 -- Solution
• Homework #6 Due Nov. 29, 2016 -- Solution
• Homework #7 Due Dec. 6, 2016 -- Solution

Exams

• Midterm 1 In class on Tuesday, October 4th.
• Midterm 2 Due Saturday, November 19, typed, in PDF format, no later than 2:30pm.
• Midterm 3 will given on December 8.
• The final exam is on December 15, but is open for negotiation.

Papers, Notes, Books and Other Resources

Papers and other notes:

• Example with Paramagnetism
• Specific Heat - Harmonic Oscillator
• Particle in a box
• Lattice Vibrations and Normal Modes; Debye Model
• Ferromagnetism and Ising Model
• Equilibrium Thermodynamic Functions; Einstein-Smoluchowski Theory of Brownian Motion; Langevin Theory of Brownian Motion
• Approach to Eq:the Fokker-Planck Equation
• Fluctuation-Dissipation Theorem

Non-equilibrium Stat Mech Reading Materials:

• Boltzmann Equation
• Lectures on The Statistical Mechanics of Irreversibility - Zwanzig. Excerpt from "Quantum Statistical Mechanics
• 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
• Statistical Mechanics of Irreversibility- Zwanzig, Excerpt from "Lectures in Theoretical Physics" Volume III - Edited by Wesley E. Brittin, B.W. Downs, and Joanne Downs
• On the Identity of Three Generalized Master Equations - Zwanzig
• Generlized Master Equation and Applications

Books

• A Modern Course in Statistical Mechanics -- Reichl
• Equilibrium and Non-Equilibrium Statistical Mechanics -- Balescu
• Statistical Mechanics -- McQuarrie
• Nonequilibrium Statistical Mechanics -- Mazenko
• 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).