Theory and numerical simulation of mass, charge, and heat transport in condensed matter
Advanced course given by Stefano Baroni, Federico Grasselli
Start: 20-04-2020 End: 15-05-2020 Room: zoom
Lectures 1-2: Introduction
- What diffusion is all about;
- Extensive variables, intensive variables, thermal equilibrium;
- Conserved densities and currents: continuity equation;
- Osmotic forces, Fick's law, and Einstein's relation between friction and diffusion coefficients;
- A mathematical intermezzo: stochastic processes and related concepts;
- Brownian motion.
Lecture 2-3: Theoretical foundations
- Hydrodynamic variables and Onsager's transport equations;
- Hamilton's and Liouville's equations of classical mechanics;
- Mixing, ergodicity, and the spectral properties of the Liouvillian
- Linear-response theory and the Green-Kubo and Einstein-Helfand expressions for transport coefficients.
Lecture 3-4: Heat transport
- Thermal vs. mechanical perturbations: heat transport;
- The classical formula for the heat current;
- Shear viscosity;
- Gauge invariance of transport coefficients;
- Quasi-harmonic theory of heat transport in crystals and glasses;
- Density-functional theory of adiabatic heat transport.
Lecture 4-5: Adiabatic charge transport
- Adiabatic charge current and Born's effective charges;
- Thouless' and Resta's topological quantization of adiabatic charge transport;
- Atomic oxidation numbers as topological charges;
- Gauge invariance and topological quantization of adiabatic charge transport.
Lectures 5-6: Computer simulations
- Computer simulations: classical and ab initio molecular dynamics;
- Data analysis for equilibrium properties: the correlation time;
- Computer simulation of transport phenomena;
- Spectral theory of time series: the Wiener-Khintchine theorem;
- Cepstral analysis for uni- and multi-variate time series.