We present time-dependent semiclassical transport models for mixed state scattering with thin quantum barriers. The idea is to use a multiscale approach to connect regions for which a classical description of the system dynamics is valid across regions for which the classical description fails, such as when the gradient of the potential is undefined. We do this by first solving a stationary Schrodinger equation in the quantum region to obtain the scattering coefficients. These coefficients allow us to build the interface condition to the particle flux, that bridges the quantum region, connecting two classical regions.
Away from the barrier, the problem may be solved by traditional numerical methods. The overall numerical cost is roughly the same as solving a classical barrier.
By using quabtum scattering data and complex Liouville equations we are even able to handle wave inteferences across the barrier.
This is a joint work with Kyle Novak.