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.s
If you enjoy the lecture notes, an expanded version is available as a textbook.
“Elegance should be left to shoemakers and tailors.”
Ludwig Boltzmann
Things Bumping Into Other Things
Introduction; Basics of Collisions; Mean Free Path; Scattering Time; Basics of Transport; Diffusion; Viscosity; Thermal Conductivity.
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.
Stochastic Processes
Brownian Motion; The Langevin Equation; Diffusion; The Einstein Relation; Noise Distributions; The Fokker-Planck Equation; Kramers-Chandrasekhar; Path Integrals, Stochastic Calculus.
Linear Response
Sources, Observables and Response Functions; Causality and Analyticity; Kramers-Kronig Relation; Dissipation; Kubo Formula; Fluctuation-Dissiptation Theorem, Response in Quantum Field Theory