A benchmark study of the signed-particle Monte Carlo algorithm for the Wigner equation
The Wigner equation is a full quantum transport model able to capture the relevant physics in next generation semiconductor devices. It is well known that the pure-state Wigner equation is an equivalent phase-space reformulation of the Schrödinger equation. At the same time the Winger equation can be augmented by a Boltzmann-like collision operator accounting for the process of decoherence. However, this equation has represented a numerically daunting task and it has raised more problems than solutions. There were a number of papers on numerical treatments of the Wigner equation. Among those there were deterministic approaches, direct simulation on the base of the Monte Carlo method, and it is often used to derive reduced transport models, such as quantum-hydrodynamic models. Here, the author focuses on the so-called signed Monte Carlo method, where the Wigner potential is treated as a scattering source which determines the elecron-potential interaction, and consequently new particles with different signs are stochastically added to the system. There were attempts of some authors to interpret the method in terms of the Markow jump process theory, producing a class of stochastic algorithms. In this article, a thorough validation of one of those algorithms is presented by comparing the Wigner MC results with the Schrödinger equation solution, in an already traditional benchmark experiment.
scientific article; zbMATH DE number 6839181
scientific article