论文标题
光谱函数的缩放渐近级
Scaling asymptotics of spectral Wigner functions
论文作者
论文摘要
我们证明，在能量级别$ e $上的平滑Wigner-Weyl光谱总和在古典能量表面上表现出渐近级别的渐近级别$σ_e$。作者早先证明了各向同性谐波振荡器，并且在本文中将证明扩展到所有量子汉密尔顿人$ - \ hbar^2δ+ v $，其中$ v $ $ v $是无限属性的限制潜力。主要工具是传播剂的Herman-kluk初始值参数和Chester-Friedman-ursell正常形式，用于具有一维立方变性的复杂阶段。这对M.V.的光谱仪分布的通风缩放渐近造型进行了严格的说明。 Berry，A。Ozoriode Almeida和其他物理学家。
We prove that smooth Wigner-Weyl spectral sums at an energy level $E$ exhibit Airy scaling asymptotics across the classical energy surface $Σ_E$. This was proved earlier by the authors for the isotropic harmonic oscillator and the proof is extended in this article to all quantum Hamiltonians $-\hbar^2 Δ+ V$ where $V$ is a confining potential with at most quadratic growth at infinity. The main tools are the Herman-Kluk initial value parametrix for the propagator and the Chester-Friedman-Ursell normal form for complex phases with a one-dimensional cubic degeneracy. This gives a rigorous account of Airy scaling asymptotics of spectral Wigner distributions of M.V. Berry, A. Ozorio de Almeida and other physicists.
