Revealing the flux: Using processed Husimi maps to visualize dynamics of bound systems and mesoscopic transport

Abstract

We elaborate upon the ``processed Husimi map'' representation for visualizing quantum wave functions using coherent states as a measurement of the local phase space to produce a vector field related to the probability flux. Adapted from the Husimi projection, the processed Husimi map is mathematically related to the flux operator under certain limits but offers a robust and flexible alternative since it can operate away from these limits and in systems that exhibit zero flux. The processed Husimi map is further capable of revealing the full classical dynamics underlying a quantum wave function since it reverse engineers the wave function to yield the underlying classical ray structure. We demonstrate the capabilities of processed Husimi maps on bound systems with and without electromagnetic fields, as well as on open systems on and off resonance, to examine the relationship between closed system eigenstates and mesoscopic transport.