Short time quantum phase space dynamics at a 1:2 Fermi resonance

Child, M. S.; Bruun, Georg M.; Paul, Rohan

doi:10.1016/0301-0104(94)00352-b

Cited by 5 publications

(3 citation statements)

References 20 publications

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“…Processed Husimi representation. -The representation of quantum-mechanical systems in terms of phase-space distribution functions, such as Wigner's quasi-probability distribution function [8,9] and the Husimi distribution function [10], allows expressing quantum-mechanical results into a form that resembles classical mechanics [11][12][13]. The standard Husimi projection technique consists of an idealized measurement of position and momentum consistent with the uncertainty principle.…”

Section: Since P2mentioning

confidence: 99%

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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Section: Since P2mentioning

confidence: 99%

Quantum flux and reverse engineering of quantum wave functions

Mason

Borunda

Heller

2013

EPL

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“…By taking snapshots of the local phase space at many points across a system for larger σ, we can produce a map of the classical trajectories that correspond to a given wavefunction. These visualizations are known as "Husimi maps" [2,[7][8][9]. Like the traditional flux map, Husimi maps can be integrated over lines and surfaces to reveal the total probability flux current.…”

Section: Definition Of the Husimi Projectionmentioning

confidence: 99%

Extending the Concept of Probability Flux

Mason,

Borunda,

Heller

2012

Preprint

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We develop the Husimi map for visualizing quantum wavefunctions 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 Husimi map is complimentary to the usual flux map, since they are identical for small coherent states. By improving our understanding of the flux operator and offering a robust and flexible alternative, we show how the Husimi projection can provide a map to the classical dynamics underlying a quantum wavefunction. We demonstrate its capabilities on bound systems with electromagnetic fields, as well as on open systems on and off resonance.

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“…We plot such sets of Husimi vectors at many points along a system, mapping the local phase space of the wave function. These visualizations are known as "Husimi maps" 3,[5][6][7] . We refer to the maps that present the complete set of Husimi vectors at each point as raw Husimi maps.…”

Section: The Processed Husimi Mapmentioning

confidence: 99%

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

2015

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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.

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Short time quantum phase space dynamics at a 1:2 Fermi resonance

Cited by 5 publications

References 20 publications

Quantum flux and reverse engineering of quantum wave functions

Quantum flux and reverse engineering of quantum wave functions

Extending the Concept of Probability Flux

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

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