Lecture Notes

Lecture notes were originally prepared by Tim Kowalczyk and Kara Manke, and updated by Chern Chuang, Thomas Avila, and Michael Mavros, 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