## Abstract

Let H denote the harmonic oscillator Hamiltonian on R^{d}, 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(λ^{d} ^{-} ^{1}) , improving in these cases the o(λ^{d} ^{-} ^{1}) remainder previously established by Helffer–Robert.

Original language | English (US) |
---|---|

Pages (from-to) | 269-294 |

Number of pages | 26 |

Journal | Communications in Mathematical Physics |

Volume | 362 |

Issue number | 1 |

DOIs | |

State | Published - Aug 1 2018 |

## ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Mathematical Physics