TY - JOUR
T1 - Refined Weyl Law for Homogeneous Perturbations of the Harmonic Oscillator
AU - Doll, Moritz
AU - Gannot, Oran
AU - Wunsch, Jared
N1 - Funding Information:
The first author was supported by the DFG GRK-1463 and would like to thank Northwestern University for its hospitality. The second and third authors gratefully acknowledge the support of NSF Grants DMS-1502632 and DMS-1600023, respectively.
PY - 2018/8/1
Y1 - 2018/8/1
N2 - 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.
AB - 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.
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U2 - 10.1007/s00220-018-3100-5
DO - 10.1007/s00220-018-3100-5
M3 - Article
AN - SCOPUS:85041553175
VL - 362
SP - 269
EP - 294
JO - Communications in Mathematical Physics
JF - Communications in Mathematical Physics
SN - 0010-3616
IS - 1
ER -