Scaling asymptotics of spectral Wigner functions*
Abstract
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 −ℏ 2Δ + 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 Berry, Ozorio de Almeida and other physicists.
Document Details
- Document Type
- Pub Defense Publication
- Publication Date
- Oct 03, 2022
- Source ID
- 10.1088/1751-8121/ac91b4
Entities
People
- Boris Hanin
- Steve Zelditch
Organizations
- National Science Foundation
- Office of Naval Research