David Tong: Lectures on Kinetic Theory
This is a graduate course on topics in non-equilibrium statistical mechanics, covering kinetic theory, stochastic processes and linear response. It is aimed at masters students and PhD students. The full set of lecture notes are around 100 pages. They can be downloaded below. Please email me if you find any typos.
A first course on statistical mechanics and thermodynamics
be found here.
- 1. Things Bumping Into Other Things:
Introduction; Basics of Collisions; Mean Free Path; Scattering Time; Basics of Transport; Diffusion; Viscosity; Thermal Conductivity.
- 2. Kinetic Theory:
BBGKY Hierarchy, Boltzmann Equation, Equilibrium and Detailed Balance, The H-Theorem, Ideal Fluids, Relaxation Time Approximation; Thermal Conductivity and Viscosity Revisited; Navier-Stokes Equation; Sound Waves.
- 3. Stochastic Processes:
Brownian Motion; The Langevin Equation; Diffusion; The Einstein Relation; Noise Distributions; The Fokker-Planck Equation; Kramers-Chandrasekhar; Path Integrals, Stochastic Calculus.
- 4. Linear Response:
Sources, Observables and Response Functions; Causality and Analyticity; Kramers-Kronig Relation; Dissipation; Kubo Formula; Fluctuation-Dissiptation Theorem, Response in Quantum Field Theory
Kinetic Theory on the Web
- Statistical Mechanics of Particles: Mehran Kardar's lectures from MIT.
- Thermodynamics and Statistical Mechanics Lecture Notes by Daniel Arovas (links directly to pdf file)
- Statistical Physics An undergraduate course by Alexander Schekochihin at Oxford
- Statistical Mechanics II A more advanced course by Joel Moore at Berkeley.
- Stochastic Processes A graduate course by Matt Scott in Waterloo.
- Introduction to Many Body Physics by Piers Coleman at Rutgers. Chapter 10 covers linear response.