Complex Diffusion Monte-Carlo method for the systems with complex wave function: test by the simulation of 2D electron in uniform magnetic field

摘要

On the base of Diffusion Monte-Carlo method it is developed a new ComplexDiffusion Monte-Carlo (CDMC) method allowing to simulate the quantum systemswith complex wave function. There are no approximations on the calculation ofmodulus and phase of wave function in contrast to other methods. We find thatthe averaged value of any quantity in CDMC will have no direct contributionfrom the phase of the distribution function but only from the phase of theGreen function of the diffusion equation. This is most important and crucialpoint of CDMC. We are testing CDMC by the calculation of the wave function andthe ground state energy of two-dimensional electron placed into the externaluniform magnetic field. There is an excellent agreement between simulationsresults and an analytical ones.