Scaling asymptotics of Wigner distributions of harmonic oscillator orbital coherent states

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