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arXiv · 2207.01677

Scaling Asymptotics of Wigner Distributions of Harmonic Oscillator Orbital Coherent States

Nicholas Lohr
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Abstract

The main result of this article gives scaling asymptotics of the Wigner distributions $W_{\varphi_N^{\gamma},\varphi_N^{\gamma}}$ of isotropic harmonic oscillator orbital coherent states $\varphi_N^{\gamma}$ concentrating along Hamiltonian orbits $\gamma$ in shrinking tubes around $\gamma$ 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 $\Sigma_E$, and a $\textit{Gaussian scaling}$ when the tube has radius $N^{-1/2}$ tangent to $\Sigma_E$.

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Nicholas Lohr. 2022-07-04. Scaling Asymptotics of Wigner Distributions of Harmonic Oscillator Orbital Coherent States. https://doi.org/10.1080/03605302.2023.2180754

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