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Algorithms and computation
Computational physics plays a central role in all fields of physics, from classical statistical physics, soft matter problems, and hard-condensed matter. Our goal is to cover the very basic concepts underlying computer simulations in classical and quantum problems, and connect these ideas to relevant contemporary research problems in various fields of physics. In the TD’s you will also learn how to set, perform and analyse simple computer simulations by yourself. We will use Python, but no previous knowledge of this programming language is needed.
Syllabus
1) Introduction to computational physics 
Brief history and examples
2) Monte Carlo methods Markov chains, Metropolis algorithm Statistical analysis of errors
3) Monte Carlo simulations of Ising models Application to Ising models and non-equilibrium phenomena
4) Monte Carlo simulations for off-latice models Some interesting details : Forces, neighbors, hard spheres Application to classical fluids
5) Molecular Dynamics Equations of motion, statistical ensembles
6) Complex and disordered systems Interesting problems and solutions : simulated annealing, parallel tempering
7) Complex situations Umbrella sampling, reweighting and phase transitions studies
8) Matrix diagonalisation in quantum physics Lanczos or Density Matrix Renormalisation Group for quantum spin systems
9) Path integral approach to quantum problems Quantum particles in arbitrary potentials
Prerequisites
Evaluation