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Simulation in Physics

Illustrating various topics in classical and quantum statistical mechanics through Monte Carlo simulations .

Physical and mathematical subjects that are addressed include:

  • Introduction to direct and Markov-chain Monte Carlo sampling
  • Equivalence of Newton and Boltzmann mechanics, classical Monte Carlo simulations
  • Entropic interactions and a liquid-gas phase transition
  • Monte Carlo integration
  • Quantum statistical mechanics: path integral representation of the density matrix, quantum Monte Carlo simulations
  • Bose-Einstein condensation
  • The Ising model of ferromagnetism

The material presented here closely follows "Statistical Mechanics: Algorithms and Computations" by W. Krauth from the École normale supérieure and "Statistical Mechanics: A Set of Lectures" by R. P. Feynman.

Path integral Monte Carlo simulations

Reference:

  1. Some resources are obtained from https://github.com/dgoekmen/Statistical-Mechanics with LISENCE retained.