6. HEURISTIC AND TOPOLOGICAL METHODS
Topologically-based methods have been used to give post-processing interpretations of velocity fields and density fields in inhomogeneous devices . For example, the presence of strong nodes in the density field gives rise to quantised vortex flow in the velocity field [21, 24, 27, 29, 60-63].
From these studies we have proposed heuristic topologically-based methods to derive ab initio velocity fields (trajectory families) which allow the incorporation of dissipative processes such as inelastic scattering, charge capture and de-trapping [22-24] using non-Hermitian effective potentials .
Simple heuristic techniques allow us to construct quantum flows from classical flows.
Confirmed by numerical simulation.
A quasi-string formalism has been devised as a computational model to show that coherent quantum states are reconstructible from a variational principle for quantum trajectories . These tools have been particularly useful in qualitative predictions of the effects of atomistic micro-variability in semiconductor devices [24, 29, 65].