Optimized Particle Regeneration Scheme for the Wigner Monte Carlo Method

Abstract

The signed-particle Monte Carlo method for solving the Wigner equation has made multi-dimensional solutions numerically feasible. The latter is attributable to the concept of annihilation of independent indistinguishable particles, which counteracts the exponential growth in the number of particles due to generation. After the annihilation step, the particles regenerated within each cell of the phase-space should replicate the same information as before the annihilation, albeit with a lesser number of particles. Since the semi-discrete Wigner equation allows only discrete momentum values, this information can be retained with regeneration, however, the position of the regenerated particles in the cell must be chosen wisely. A simple uniform distribution over the spatial domain represented by the cell introduces a ‘numerical diffusion’ which artificially propagates particles simply through the process of regeneration. An optimized regeneration scheme is proposed, which counteracts this effect of ‘numerical diffusion’ in an efficient manner.