Spectral asymptotics of semiclassical unitary operators

Yohann Le Floch (1) , Alvaro Pelayo (2)

1 IRMA - Institut de Recherche Mathématique Avancée
2 UC San Diego - University of California [San Diego]

This paper establishes an aspect of Bohr's correspondence principle, i.e. that quantum mechanics converges in the high frequency limit to classical mechanics, for commuting semiclassical unitary operators. We prove, under minimal assumptions, that the semiclassical limit of the convex hulls of the quantum spectrum of a collection of commuting semiclassical unitary operators converges to the convex hull of the classical spectrum of the principal symbols of the operators.

Mots clés: spectral theory; semiclassical analysis; symplectic actions

Domaines: Théorie spectrale [math.SP]; Géométrie symplectique [math.SG]; Equations aux dérivées partielles [math.AP]

Yohann Le Floch, Alvaro Pelayo. Spectral asymptotics of semiclassical unitary operators. Journal of Mathematical Analysis and Applications, 2019, ⟨10.1016/j.jmaa.2019.01.015⟩. ⟨hal-01161621v3⟩