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 wavefunction 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.

Valley-dependent time evolution of coherent electron states in tilted anisotropic Dirac materials

“…On the other hand, the Wigner function (WF) approach has been a powerful physical tool in quantum optics [51][52][53][54][55][56][57], which has been applied recently also in condensed matter in the study of electron dynamics in two-dimensional materials, particularly in graphene and under the presence of electromagnetic fields [18,56,[58][59][60][61][62][63][64][65][66][67][68][69][70]. The recent advances in the experimental reconstruction of the WF of electronic systems could bring the possibility of the realization of coherent electron states in the laboratory and the development of electron quantum optics [59,71,72].…”

Ballistic electron transport in graphene nanodevices and billiards

“…Surprisingly however, this is not at all the case. Only very recently Mason et al introduced the Husimi functions for studying nanodevices [92,93,94], in an approach aiming to visualize classical paths inside the device. More in-depth analysis of classical concepts (e.g.…”

“…This (I believe) is the reason that it has been used extensively in numerous fields such as quantum optics [79,80,78], ocean acoustics [81] and quantum chaos [82,83,84,85,86,87,88,89,90,91]. Adaptation in condensed matter physics is still lagging behind other fields, as only recently the Husimi function has been used to study nanodevices [92,93,94].…”

“…Mason, Borunda and Heller have also used the Husimi function recently in condensed matter systems [92,93,94]. The extended the Husimi function, defining the Husimi processed map, which is a tool that allows one to visualize classical paths in nanodevices.…”

“…A the vector potential. Mason, Borunda and Heller have suggested in [94] that one should use the same transformation for the wavepacket, k 0 → k 0 − c q A/ .…”