Microscopic Theory of Transport

Lecture Notes

DAY #	TOPICS
1	Course Overview and Introduction (PDF)
Part I - Correlation Functions
2	Diffusion: mean square displacement (PDF)
3	Diffusion: velocity autocorrelation - Green Kubo relations (PDF)
4	Diffusion: Van Hove self correlation function Gs(r,t) (PDF)
5	The density correlation function G(r,t) (PDF)
6	Properties of time correlation functions (PDF)
7	The radial distribution function g(r)
8	Dynamic structure factor and inelastic neutron and light scattering
9	Equations for G(r,t) and phase-space correlation
10	Equations of hydrodynamics
11	Hydrodynamic theory of dynamic structure factor
Part II - Kinetic Theory
12	Boltzmann equation: brief derivation
13	Boltzmann equation: collisional invariants and hydrodynamic limit
14	Continuation of Lecture 13
15	Boltzmann equation: H-theorem and equilibrium solution
16	Linearized Boltzmann equation: relaxation time models
17	Kinetic theory of Gs(r,t) - Nelkin-Ghatak model
18	Continuation of Lecture 17
19	Kinetic theory of G(r,t): BGK model
20	Kinetic models, Boltzmann equation and neutron transport equation
21	Linear response theory - complex susceptibility, fluctuation-dissipation theorem
22	Continuation of Lecture 21
Part III - Atomistic Simulation of Transport and Related Phenomena
23	Mean Free Path Treatment of Transport (viscosity, conductivity, diffusion)
24	Continuation of Lecture 22
25	Role of atomistic simulations in transport (PDF)
26	Basic Molecular Dynamics: time integration, potential, book keeping, flow chart, unique properties
27	Continuation of Lecture 26
28	Atomistic simulation of liquids - structure and dynamics
29	Transport phenomena beyond Boltzmann - cage effects, molasses tail, phonon lifetimes
30	Diversity of atomistic simulation applications (concepts)
31	Thermal conductivity of a solid (SiC)
32	MD studies of phase transitions - melting, vitrification and amorphization
33	Continuation of Lecture 32
34	Multiscale materials modeling - perspective and visualization
35	Final topic on transport theory: memory function, mode coupling