A Coherent Semiclassical Transport Model for Pure-state Quantum Scattering∗

We present a time-dependent semiclassical transport model for coherent pure-state scattering with quantum barriers. The model is based on a complex-valued Liouville equation, with interface condition at quantum barriers using complex-valued scattering coefficients computed from the steady-state Schrödinger equation. By retaining the phase information at the barrier, this coherent model is adequate in describing quantum scattering and interference at quantum barriers, with a computational cost comparable to that of the classical mechanics. We construct both Eulerian and Lagrangian numerical methods for this model, and validate it using several numerical examples, including resonant multiple quantum barriers.