Syllabus
* Phase transitions and critical phenomena
Methods of inserting particles, Gibbs ensemble, phase equilibrium, critical temperature by scaling with a system size, critical slowing down, cluster algorithms for spin models.
* Simulation of realistic systems
Long-range forces, Ewald summation, simulation of molecular systems, methods conserving bond length and angles, phase equilibrium.
* Special algorithms and techniques
Random number generation, multispin coding for Ising model and cellular automata, multiscale simulations.
* Non-equilibrium systems close to equilibrium
Calculation of kinetic coefficients, time correlation functions, Einstein relation, non-equilibrium MD, self-diffusion in lattice gas, equilibrium and con-equilibrium calculation of viscosity and dielectric constant.
* Kinetic Monte Carlo
Choice of kinetics and rates, time in kinetic MC, "n-fold way" algorithm, model of adsorption and desorption.
* Simulation of growth processes
Simulation of simple growth models (Eden, Edwars-Wilkinson model etc.), kinetic roughening, Laplacian growth, diffusion limited aggregation (DLA), solid-on-solid models, realistic simulations of crystal growth.
* Optimalization problems
Traveling salesman problem, simulated annealing, calculation of diffusion in lattice gas, calculation of energy barriers by molecular statics, finding the minimal energy path in a system on N particles, method "elastic nudged band".
* Quantum simulations
Variational quantum MC, canonical quantum MC, isomorphism of quantum and classical systems, sign problem, first principle calculations, method of density functional.
Annotation
Advanced Monte Carlo and molecular dynamics methods, their application to critical, nonequilibrium and quantum systems: cluster algorithms for lattice models, transport coefficients, kinetic MC, quantum Monte Carlo, simulations from the first principles. Suitable for the 1st and 2nd year of master's studies and for doctoral students in the fields of theoretical physics and mathematical modeling.