Refined Weyl Law for Homogeneous Perturbations of the Harmonic Oscillator

Moritz Doll*, Oran Gannot, Jared Wunsch

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

4 Scopus citations


Let H denote the harmonic oscillator Hamiltonian on Rd, perturbed by an isotropic pseudodifferential operator of order 1. We consider the Schrödinger propagator U(t) = e- i t H, and find that while sing - supp Tr U(t) ⊂ 2 πZ as in the unperturbed case, there exists a large class of perturbations in dimensions d≥ 2 for which the singularities of Tr U(t) at nonzero multiples of 2 π are weaker than the singularity at t = 0. The remainder term in the Weyl law is of order o(λd - 1) , improving in these cases the o(λd - 1) remainder previously established by Helffer–Robert.

Original languageEnglish (US)
Pages (from-to)269-294
Number of pages26
JournalCommunications in Mathematical Physics
Issue number1
StatePublished - Aug 1 2018

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics

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