Quantum mechanics simulated by diffusion and branching processes

Abstract

The imaginary time Schrödinger-equation can be simulated by a diffusion process, which reflects the kinetic energy operator, and a branching process arising from the potential energy. We use this well known facts to simulate quantum-mechanical systems by an embedding algorithm, which allows very fast simulations without an infinitesimal time step. The internal variables do not only represent single states of Brown’ian particles but complete ensembles of randomwalkers. Thus the algorithm is efficient not only because the time evolution is fast, moreover the averaging results in excellent statistics for the expectation values.