Coherence and Spatial Resolution of Transport in Quantum Cascade Lasers

The method of nonequilibrium Greens functions allows for a spatial and energetical resolution of the electron current in Quantum Cascade Lasers. While scattering does not change the spatial position of carriers, the entire spatial evolution of charge can be attributed to coherent transport by complex wave functions. We discuss the hierarchy of transport models and derive the density matrix equations as well as the hopping model starting from the nonequilibrium Greens functions approach.