A high order local solver for Wigner equation

In the modeling of nanoscale heterogeneous structure, quantum effects must be included. Several approaches have been suggested such as density matrix, non-equilibrium Green´s function and phase space Wigner formalism. Among them Wigner function formalism is suitable for describing time dependent dynamics and connecting quantum and semi-classical regimes. We present here a new deterministic solver for Wigner equations. High order numerical discretization is employed in order to minimize the spurious numerical dissipation and dispersion. Semi-classical boundary condition is enforced thanks to suitable localization of the Wigner integral kernel. The accurate quantum interference is captured when compared with the corresponding Schrodinger simulation.