A semiclassical transport model for two-dimensional thin quantum barriers

We present a two-dimensional time-dependent semiclassical transport model for mixed-state scattering with thin quantum films. The stationary Schrödinger equation is solved in the quantum barrier to obtain the scattering coefficients used to supply the interface condition that connects two classical domains. The solution in the classical regions is solved using a particle method and interface condition combined with the Hamiltonian-preserving scheme. The overall cost is roughly the same as solving a classical barrier. We construct a numerical method based on this semiclassical approach and validate the model using two numerical examples.