论文标题
谐波振荡器轨道相干状态的WIGNER分布的缩放渐近分布式
Scaling Asymptotics of Wigner Distributions of Harmonic Oscillator Orbital Coherent States
论文作者
论文摘要
本文的主要结果给出了Wigner分布的缩放缩放级别$ w_ {φ_n^γ，φ_n^γ} $的各向同性谐波振荡器轨道相干状态$φ_n^γ$集中在沿Hamiltonian Orbits Orbits $γ$γ$γ$γ$γ$γ$ guninking $γ$中。特别是，这些Wigner分布显示出$ \ textit {hybrid} $半古典缩放。也就是说，同时，当试管具有半径$ n^{ - 2/3} $时，我们有一个$ \ textIt {airy缩放} $，当试管带有半径$ n^radius $ n^{ - 1/2} $ pentent $ n^$ n^{ - 1/2} $ pentent $ pentent $ content $ $ content $ $ content $ $ content $ $ content $ $ n^$ n^gaussian缩放} $。
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 $Σ_E$.
