Douglas J. Mason

Threshold for Chaos and Thermalization in the One-Dimensional Mean-Field Bose-Hubbard Model

We study the threshold for chaos and its relation to thermalization in the 1D mean-field Bose-Hubbard model, which, in particular, describes atoms in optical lattices. We identify the threshold for chaos, which is finite in the thermodynamic limit, and show that it is indeed a precursor of thermalization. Far above the threshold, the state of the system after relaxation is governed by the usual laws of statistical mechanics.

Semiclassical deconstruction of quantum states in graphene

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.

Quantum flux and reverse engineering of quantum wave functions

An interpretation of the probability flux is given, based on a derivation of its eigenstates and relating them to coherent-state projections on a quantum wave function. An extended definition of the flux operator is obtained using coherent states. We present a “processed Husimi” representation, which makes decisions using many Husimi projections at each location. The processed Husimi representation reverse engineers or deconstructs the wave function, yielding the underlying classical ray structure. Our approach makes possible interpreting the dynamics of systems where the probability flux is uniformly zero or strongly misleading. The new technique is demonstrated by the calculation of particle flow maps of the classical dynamics underlying a quantum wave function in simple model systems such as a circular billiard with and without a magnetic field.