Statistical Mechanics PDF

Statistical Mechanics

Course Description

This course discusses the principles and methods of statistical mechanics. Topics covered include classical and quantum statistics, grand ensembles, fluctuations, molecular distribution functions, other concepts in equilibrium statistical mechanics, and topics in thermodynamics and statistical mechanics of irreversible processes.

Lecture Notes

The lecture notes were prepared by Tim Kowalczyk and Kara Manke in collaboration with Professor Cao.

CHAPTER #	TOPICS	SUBTOPICS
1	Stochastic Processes and Brownian Motion (PDF)	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 (PDF)	2.1 Response, Relaxation, and Correlation 2.2 Onsager Regression Theory 2.3 Linear 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 (PDF)	3.1 Light Scattering 3.2 Navier-Stokes Hydrodynamic Equations 3.3 Transport Coefficients
4	Time Correlation Functions (PDF)	4.1 Short-time Behavior 4.2 Projection Operator Method 4.3 Viscoelastic Model 4.4 Long-time Tails and Mode-coupling Theory