Scaling asymptotics of Wigner distributions of harmonic oscillator orbital coherent states

Abstract

Abstract The main result of this article gives scaling asymptotics of the Wigner distributions of isotropic harmonic oscillator orbital coherent states concentrating along Hamiltonian orbits γ in shrinking tubes around γ in phase space. In particular, these Wigner distributions exhibit a hybrid semi-classical scaling. That is, simultaneously, we have an Airy scaling when the tube has radius normal to the energy surface Σ E , and a Gaussian scaling when the tube has radius tangent to Σ E .