The Role of Annihilation in a Wigner Monte Carlo Approach
The Wigner equation provides an interesting mathematical limit, which recovers the constant field, ballistic Boltzmann equation. The peculiarities of a recently proposed Monte Carlo approach for solving the transient Wigner problem, based on generation and annihilation of particles are summarized. The annihilation process can be implemented at consecutive time steps to improve the Monte Carlo resolution. We analyze theoretically and numerically this process applied to the simulation of important quantum phenomena, such as time-dependent tunneling of a wave packet through potential barriers.
This work has been supported by the the project EC AComIn (FP7-REGPOT-2012-2013-1), and Bulgarian NSF Grants DTK 02/44/2009 and Austrian Science Fund Project FWF-P21685-N22.