
arXiv: 2207.01677
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
Mathematics - Spectral Theory, FOS: Mathematics, FOS: Physical sciences, Mathematical Physics (math-ph), Spectral Theory (math.SP), Mathematical Physics
Mathematics - Spectral Theory, FOS: Mathematics, FOS: Physical sciences, Mathematical Physics (math-ph), Spectral Theory (math.SP), Mathematical Physics
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