FSI3250 Advanced Simulation Methods in Statistical Physics 7.5 credits

• Basics of molecular dynamics
• Basics of Monte Carlo simulations
• Markov chain theory
  • Detailed balance, Metropolis method, Heat bath method, etc
  • Convergence
  • Dynamical point of view, simulating rare events using N-fold way
• Data analysis:
  • Estimating errors. Autocorrelation times.
  • Histogram reweighting
• Simulations in different ensembles:
  • MC in NPT, Grand canonical, (Micro canonical) ensembles
  • MD in Canonical, NPT ensembles, etc
• Simulations in extended ensembles:
  • Parallel tempering (aka Replica exchange MC)
  • Multicanonical, Simulated tempering, …
  • Wang-Landau method
• Free energy calculations
  • Integration method (temperature, density, or other parameters)
  • Umbrella sampling
  • Particle insertion
• Cluster updates and worm algorithms
  • Swendsen-Wang, Wolff
• Quantum Monte Carlo:
  • Path integral MC: Mapping to classical problem
  • Stochastic series expansion (SSE)
  • Worm algorithm

After completed course, the PhD student should:

• have a deep theoretical understanding of several Monte Carlo and molecular dynamics methods.
• have hands-on experience from implementing and using these techniques.
• be able carry out simulations in different ensembles.
• be able to carry out advanced data analysis using, e.g., reweighting.
• know when to apply the different methods.
• be able to develop new simulation methods.

Familiarity with computers and basic programming ability.
Basic statistical physics.
Elementary probability theory.
Basic course in computer simulations recommended, but not compulsory.

There is no specific course textbook. The course literature consists of lecture notes and several research articles as well as several textbooks can be used.

Based on recommendation from KTH’s coordinator for disabilities, the examiner will decide how to adapt an examination for students with documented disability.

The examiner may apply another examination format when re-examining individual students.

If the course is discontinued, students may request to be examined during the following two academic years.

To fulfill the course requirements you should complete the computer labs/projects and give a short presentation (15-20 min) of a special topic of your choice.

• All members of a group are responsible for the group's work.
• In any assessment, every student shall honestly disclose any help received and sources used.
• In an oral assessment, every student shall be able to present and answer questions about the entire assignment and solution.