CONVERGENCE OF THE MONTE-CARLO ALGORITHM FOR THE SOLUTION OF THE WIGNER QUANTUM-TRANSPORT EQUATION

The Wigner function provides a convenient description for single-parti cle quantum transport in space dependent systems, such as modern nanoe lectronic devices. A Monte Carlo algorithm has been recently introduce d for the solution of this integro-differential equation. However, whe n the potential applied to the system has different limits at + and -i nfinity, a convergence problem arises for the kernel of the integral p art of the equation. In this paper, we discuss the rigorous mathematic al aspects of the convergency of the solution of the Wigner equation a nd of the Neumann expansion on which the Monte Carlo algorithm is base d.