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.
ASJC Scopus subject areas
- Statistical and Nonlinear Physics
- Mathematical Physics