A Semiclassical Transport Model for Thin Quantum Barriers

We present a one-dimensional time-dependent semiclassical transport model for mixed state scattering with thin quantum barriers. The idea is to solve a stationary Schr6dinger equation in the thin quantum barrier to obtain the scattering coefficients, and then use them to supply the interface condition that connects the two classical domains. We then build in the interface condition to the numerical flux, in the spirit of the Hamiltonian-preserving scheme introduced by Jin and Wen for a classical barrier. 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 various numerical examples.