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Course Description
In this course we will discuss principles and methods of statistical mechanics. Topics will include: classical and quantum statistics, grand ensembles, fluctuations, molecular distribution functions, and other topics in equilibrium statistical mechanics. Topics in thermodynamics and statistical mechanics of irreversible processes will also be covered.
Prerequisites
5.70 Statistical Thermodynamics with Applications to Biological Systems
5.73 Introductory Quantum Mechanics I
18.075 Advanced Calculus for Engineers
Textbooks
The following is a list of recommended textbooks that you may find useful for this course. No required readings will be assigned.
Groot, Sybren Ruurds de, and Peter Mazur. Non-Equilibrium Thermodynamics. New York, NY: Dover Publications, 1984. ISBN: 9780486647418.
van Kampen, N. G. Stochastic Processes in Physics and Chemistry. Boston, MA: Elsevier, 2007. ISBN: 9780444529657.
Boon, Jean-Pierre, and Sidney Yip. Molecular Hydrodynamics. New York, NY: McGraw-Hill, 1980. ISBN: 9780070065604.
Reichl, Linda E. A Modern Course in Statistical Physics. New York, NY: Wiley, 1998. ISBN: 9780471595205.
Hansen, Jean-Pierre, and Ian R. McDonald. Theory of Simple Liquids. Burlington, MA: Elsevier Academic Press, 2006. ISBN: 9780123705358.
McQuarrie, Donald A. Statistical Mechanics. Sausalito, CA: University Science Books, 2000. ISBN: 9781891389153.
Assignments
There will be 4 problem sets assigned. They will be graded.
Final Project
You will have to complete a final project at the end of the term. You will be given a set of problems to work on outside of class.
Grading
This course will be graded based on the following:
Grading criteria.
| ACTIVITIES |
PERCENTAGES |
| Class participation |
10% |
| Four problem sets |
50% |
| Final project |
40% |
Calendar
Course calendar.
| CHAPTER # |
TOPICS |
SUBTOPICS |
| 1 |
Stochastic Processes and Brownian Motion |
1.1 Markov Processes
1.1.1 Probability Distributions and Transitions
1.1.2 The Transition Probability Matrix
1.1.3 Detailed Balance
1.2 Master Equations
1.2.1 Motivation and Derivation
1.2.2 Mean First Passage Time
1.3 Fokker-Planck Equations
1.3.1 Motivation and Derivation
1.3.2 Properties of Fokker-Planck Equations
1.4 The Langevin Equation
1.5 Appendix: Applications of Brownian Motion
|
| 2 |
Non-equilibrium Thermodynamics |
2.1 Response, Relaxation, and Correlation
2.2 Onsager Regression Theory
2.3 Response Response Theory and Causality
2.3.1 Response Functions
2.3.2 Absorption Power Spectra
2.3.3 Causality and the Kramers-Kronig Relations
|
| 3 |
Hydrodynamics and Light Scattering |
3.1 Light Scattering
3.2 Navier-Stokes Hydrodynamic Equations
3.3 Transport Coefficients
|
| 4 |
Time Correlation Functions |
4.1 Short-time Behavior
4.2 Projection Operator Method
4.3 Viscoelastic Model
4.4 Long-time Tails and Mode-coupling Theory
|