Refined Weyl law for the perturbed harmonic oscillator
Lundi, 11 Février, 2019 - 13:30
We consider the quantum harmonic oscillator H0=(-Δ+|x|2)/2. The underlying classical flow is periodic with period 2π. By an explicit calculation one can see that the Schrödinger propagator of H0 is the identity (modulo a sign) at 2π\ℤ and locally smoothing otherwise.
This periodicity is related to a sharp remainder estimate for the counting function of the eigenvalues of H0. If we perturb the operator by a pseudodifferential operator of lower order, then we break the symmetry and could hope for an improved remainder estimate. We will present results on recurrence of singularities for these operators as well as an improved remainder estimate.
This is based on joint work with Oran Gannot, Jared Wunsch, and Steve Zelditch.
Institution de l'orateur :
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Salle 1, Tour IRMA