A Weight Decomposition Approach to the Sign Problem in Wigner Transport Simulations

A stochastic method for simulation of carrier transport in semiconductor nanostructures is presented. The Wigner formulation of quantum mechanics is used. The method which aims at evaluation of mean values of physical quantities, is obtained by following the rules of the Monte Carlo theory. A particular numerical feature of the method are statistical weights with inverse signs which can achieve large absolute values. They give rise to high variance of the simulation results, the so called sign problem in quantum Monte Carlo simulations. A weight decomposition approach is proposed which limits the value of a weight by storing part of it on a phase space grid. Annihilation of positive and negative stored weights, which occur during the simulation significantly improves the variance of the method.