Self-Energy Concept for the Numerical Solution of the Liouville-von Neumann Equation

A new numerical approach is presented for the determination of the statistical density matrix as a solution of the Liouville-von Neumann equation in center-mass coordinates. The numerical discretization is performed by utilizing a finite volume method, which leads to a discretized drift and diffusion operator. The solution is based on the eigenvector basis of the discretized diffusion operator with its corresponding eigenvalues and on the introduction of the self-energy concept. More specifically, the selfenergy concept is essential to describe open-boundary problems adequately. Furthermore, this approach allows the definition of inflow and outflow conditions. The method presented is investigated with regard to the conventional Wigner transport equation and the quantum transmitting boundary method, when investigating coherent effects.