Extending the Concept of Probability Flux

Mason, Douglas J.; Borunda, Mario F.; Heller, Eric J.

doi:10.48550/arxiv.1205.3708

Cited by 4 publications

(12 citation statements)

References 21 publications

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“…Efforts, however, have been seen in the literature attempting to extend the standard concept of the probability current, e.g. by the group of E. J. Heller at Harvard University [52][53][54].…”

Section: B Some Critical Remarksmentioning

confidence: 99%

Extended virtual detector theory including quantum interferences

Xu¹,

Xu²,

Eberly³

2020

Preprint

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We extend our earlier "virtual detector" method [X. Wang, J. Tian, and J. H. Eberly, Phys. Rev. Lett. 110, 243001 (2013)], a hybrid quantum mechanical and classical trajectory method, to include phases in the classical trajectories. Effects of quantum interferences, lost in the earlier method, are restored. The obtained photoelectron momentum distributions agree well with the corresponding numerical solutions of the time-dependent Schrödinger equation.

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Section: B Some Critical Remarksmentioning

confidence: 99%

Extended virtual detector theory including quantum interferences

Xu¹,

Xu²,

Eberly³

2020

Preprint

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“…Building off work in Husimi [2] and Mason et al [3], we define the Husimi function as a measurement between a wavefunction ψ ({r i }) and a coherent state |r 0 , k 0 , σ , which minimizes joint uncertainty in spatial and momentum coordinates. For lattice systems, the wavefunction represents the probability amplitude multiplier of localized wavefunctions indexed at discrete lattice sites, which are associated with discrete positions in the set {r i }.…”

Section: A Definition Of the Husimi Projectionmentioning

confidence: 99%

“…Earlier work has shown that for σk 1, Eq. 5 is proportional to the traditional flux vector expectation value [3]. For lattice systems, the traditional flux becomes a finite-difference approximation defined by the lattice.…”

Section: A Definition Of the Husimi Projectionmentioning

confidence: 99%

“…In the original introduction of the Husimi map [3], each Husimi function is weighted by the wavevector of the coherent state to produce a visual guide to the classical dynamics of the system. Summing all the vectors equates to the flux operator (Eq.…”

Section: Group Velocitymentioning

confidence: 99%

“…Later work [3] further developed the numerical framework of the Husimi map and applied it to a wider variety of systems by incorporating local potentials and examining flux through open systems. This article expands the Husimi map technique from continuous, free-particle systems like the twodimensional electron gas (2DEG) to crystalline systems like graphene.…”

Section: Introductionmentioning

confidence: 99%

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Husimi Maps in Lattices

Mason,

Borunda,

Heller

2012

Preprint

Self Cite

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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.

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Quantum flux and reverse engineering of quantum wave functions

Mason

Borunda

Heller

2013

EPL

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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 wavefunction. 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 wavefunction, 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 wavefunction in simple model systems such as a circular billiard with and without a magnetic field.

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Extending the Concept of Probability Flux

Cited by 4 publications

References 21 publications

Extended virtual detector theory including quantum interferences

Extended virtual detector theory including quantum interferences

Husimi Maps in Lattices

Quantum flux and reverse engineering of quantum wave functions

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