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Communications in Partial Differential Equations
Article . 2023 . Peer-reviewed
Data sources: Crossref
https://dx.doi.org/10.48550/ar...
Article . 2022
License: CC BY
Data sources: Datacite
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Scaling asymptotics of Wigner distributions of harmonic oscillator orbital coherent states

Authors: Lohr, Nicholas;

Scaling asymptotics of Wigner distributions of harmonic oscillator orbital coherent states

Abstract

The main result of this article gives scaling asymptotics of the Wigner distributions $W_{φ_N^γ,φ_N^γ}$ of isotropic harmonic oscillator orbital coherent states $φ_N^γ$ concentrating along Hamiltonian orbits $γ$ in shrinking tubes around $γ$ in phase space. In particular, these Wigner distributions exhibit a $\textit{hybrid}$ semi-classical scaling. That is, simultaneously, we have an $\textit{Airy scaling}$ when the tube has radius $N^{-2/3}$ normal to the energy surface $Σ_E$, and a $\textit{Gaussian scaling}$ when the tube has radius $N^{-1/2}$ tangent to $Σ_E$.

22 pages, 7 figures

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Keywords

Mathematics - Spectral Theory, FOS: Mathematics, FOS: Physical sciences, Mathematical Physics (math-ph), Spectral Theory (math.SP), Mathematical Physics

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
1
Average
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