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- W4288804749 abstract "We prove that smooth Wigner-Weyl spectral sums at an energy level $E$ exhibit Airy scaling asymptotics across the classical energy surface $Sigma_E$. This was proved earlier by the authors for the isotropic harmonic oscillator and the proof is extended in this article to all quantum Hamiltonians $-hbar^2 Delta + V$ 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." @default.
- W4288804749 created "2022-07-30" @default.
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- W4288804749 date "2022-07-27" @default.
- W4288804749 modified "2023-09-29" @default.
- W4288804749 title "Scaling asymptotics of spectral Wigner functions" @default.
- W4288804749 doi "https://doi.org/10.48550/arxiv.2207.13571" @default.
- W4288804749 hasPublicationYear "2022" @default.
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