Lecture Notes

Fall 2020 Lecture Notes

Module 1: Kinetic Theory

Lecture 1a: Review of Hamiltonian Mechanics

Lecture 1b: Basic Hamiltonian Chaos

Supplement 1: Chirikov, Chaos and KAM → an OV

Supplement 2: Tori and their Destruction

Lecture 2a: Deriving the Boltzmann Equation

Lecture 2b: H-Theorem

Lecture 2c: Boltzmann Eqn, Entropy, Cont'd

Lecture 3a: Deriving Fluid Equations

Lecture 3b: Macroscopics of Fluids

Lecture 4a: Transport Coefficients and Viscous Fluids

Recorded Lecture on Fluids

Lecture 4b: Transport Coefficients and Entropy Production

Lecture 4b: Addendum on Up Gradient Transport

Lecture 4c: Entropy Production and Onsager Symmetry

Lecture 4c: Entropy Production and Onsager Symmetry

Module 2: Statistical Dynamics I

Lecture 5a: Brownian Motion and Langevin Eqn

Lecture 5b: Langevin Dynamics, Cont'd

Lecture 6a: Fokker-Planck 1

Lecture 6b: Fokker-Planck 2

Lecture 7a: Central Limit Theorem and Beyond 1

Lecture 7b: Central Limit Theorem and Beyond 2

Lecture 8: Kramers Problem and First Passage

Module 3: Linear Response — Kubo Formalism (Classical, QM), Landau Problem, Quasilinear Theory

Lecture 9a: Linear Response and Kubo Formalism 1

Lecture 9b: Linear Response and Kubo Formalism 2

Lecture 10a: Plasmas on a B-O-E

Lecture 10b: Vlasov Equation and Landau Problem

Lecture 10c: Quasilinear Mean Field Theory

Supplement 1a: Hydrodynamic Equations Repost

Supplement 1b: Hydrodynamic Equations Correlations

Module 4: Statistical Dynamics II

Lecture 11a: Master Equation and Appl.

Lecture 11b: Aggregation

Lecture 11c: Aggregation and Gelation

Lecture 12: Kramers, Weak Friction

Module 5: Toward Renormalization: Projection, MZT and Mode–Mode Coupling

Lecture 13a: Mori-Zwanzig Theory

Lecture 13b: Renormalization and Mode–Mode Coupling

Fall 2019 Lecture Notes

Notes 1, Section 1: Boltzmann Equation — posted 03 Oct 2019

Notes 1, Section 2: Boltzmann H-Theorem — posted 03 Oct 2019

Notes 1, Section 3: Fluid Equations and Transport Coefficents — posted 07 Oct 2019

Notes 1, Section 4: Moment Closure Approach to Transport Coefficients — posted 10 Oct 2019

Notes 1, Section 5: Detailed Chapman–Enskog Transport Calculation — posted 10 Oct 2019

Notes 1, Section 6: Onsager Symmetry — posted 14 Oct 2019

Notes 2, Section 1: Kubo Formulae: for Conductivity and Diffusion — revised version posted 17 Oct 2019

Notes 2, Section 2: Hydrodynamic Equations and Correlation Functions I — revised version posted 28 Oct 2019

Notes 2, Section 3: Hydrodynamic Equations and Correlation Functions II — posted 28 Oct 2019

Notes 3, Section 1: Langevin Equation and its Application; Fluctuation–Dissipation Theorem — posted 15 Nov 2019

Notes 3, Section 2: Fokker–Plank Theory, Additive and Multiplicative Noise — posted 15 Nov 2019

Notes 3, Section 3: Kramers Problem, Barrier Passage, F-P Reformulation — revised version posted 18 Nov 2019

Notes 3, Section 4: First Passage, Theory of Aggregation and Coagulation — revised version posted 21 Nov 2019

Notes 4: Master Equation — Basics and Quantum — posted 02 Dec 2019

Notes 5: Non-Markovian Stochastic Processes and Zwanzig–Mori Theory — posted 02 Dec 2019

Notes 6: Coarsening—Macroscopics, Section 1; Basics and Non-Conservative Models — posted 05 Dec 2019