A sensitivity study of the Wigner Monte Carlo method

Recently a Wigner Monte Carlo technique exploiting the concept of signed particles has been developed for time dependent, multi-dimensional simulations of quantum mechanical effects in the ballistic regime. This method is based on the introduction of a semi-discrete phase-space which involves a free parameter LC defining the discretization of the space of momenta. A systematic study to understand how the quality and reliability of the solution is influenced by this parameter is necessary. In this work, we analyze the sensitivity of the Wigner Monte Carlo method on LC. To this aim, three quality measures are introduced based on a comparison with the Schrödinger equation (considered as a benchmark model in this work). We show that, essentially, the Wigner Monte Carlo method is not affected by the choice of LC. Indeed, a large range of valid choices is available which demonstrates the robustness and reliability of the method.