Quantum Monte Carlo: from Stochastic Processes to Many-Body Physics

"The Monte Carlo methods, which use stochastic processes to sample random variables in the configuration space, have been very productive for a broad class of problems in classical physics. Recently a series of stochastic methods, called quantum Monte Carlo, have been developed to calculate physical properties of quantum many-body systems. Their thermodynamic quantities can be computed with path-integral Monte Carlo which is based on Feynmans original idea of mapping path integrals of a quantum system onto interacting classical polymers. The variational and diffusion Monte Carlo methods enable one to calculate accurate ground-state (T=0) properties of a many-body system. Starting from the basic concepts in the probability theory, we here review the general formalism of these powerful numerical methods and present some interesting applications of theirs with emphasis on superfluid phenomena in bosonic systems. "