Quantum Corrections to Semiclassical Transport in Nanoscale Devices using Entropy Principles

We derive a modification of the semiclassical Fermi Golden Rule collision operator based on quantum thermodynamic principles. The resulting operator is nonlocal in space and acknowledges the presence of steep potential gradients and potential barriers. The resulting quantum mechanical transport equation the Wigner quantum Boltzmann equation increases the corresponding quantum mechanical entropy and is therefore well posed.