METHODS OF COMPUTATIONAL PHYSICS
Lecture Notes
- Introduction: notes;
slides;
see F. Wilczek,
Physics in 100 years, Phys. Today 69(4), 32 (2016)
- Monte Carlo basics;
slides
- Monte Carlo simulation of spins;
slides;
Metropolis Monte Carlo Q&A
- Advanced Monte Carlo algorithms
- Numerical integration and Gaussian quadratures;
Numerical Recipes, Sec. 4.5
- Molecular dynamics basics;
slides;
Q&A;
see
Michael Levitt's Nobel lecture in 2013
- Quantum dynamics basics: splitting-operator and spectral methods;
slides;
Fourier transform (Numerical Recipes, Sec. 12.1) and
fast Fourier transform (Numerical Recipes, Sec. 12.2)
- Iterative energy minimization for quantum molecular dynamics;
Numerical Recipes, Sec. 10.6 on the conjugate-gradient method;
see CSCI 699: Extreme-scale Quantum Simulations
- Tight binding model of electronic structures;
slides
- Eigensystems;
slides
- Newton method for root finding;
slides
- Singular value decomposition and density matrix;
slides;
Numerical Recipes, Sec. 2.6
- Lanczos method for eigensystems (slides and
supplementary notes)
- Cholesky decomposition
(notes and
Numerical Recipes, Sec. 2.9)
- Monte Carlo simulation of stochastic processes;
slides
- Quantum Monte Carlo simulation;
slides;
see public-domain QMC & related software -- QMCPACK,
QWalk,
CASINO &
NetKet
- Kinetic Monte Carlo simulation and transition state theory;
motivating slides;
electron-transfer simulation;
suppl. 1: Liouville equation;
suppl. 2: master equation;
suppl. 3: transition state theory;
suppl. 4: kinetic Monte Carlo simulation
- Quantum computing;
quantum gates and circuits;
transverse-field Ising model
- Miscellaneous lectures: