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Husimi Maps in Lattices
We build upon previous work that used coherent states as a measurement of the
local phase space and extended the flux operator by adapting the Husimi
projection to produce a vector field called the Husimi map. In this article, we
extend its definition from continuous systems to lattices. This requires making
several adjustments to incorporate effects such as group velocity and multiple
bands. Several phenomena which uniquely occur in lattice systems, like
group-velocity warping and internal Bragg diffraction, are explained and
demonstrated using Husimi maps. We also show that scattering points between
bands and valleys can be identified in the divergence of the Husimi map