The wave trace and resonances of the magnetic Hamiltonian with singular vector potentials

Abstract

We study leading order singularities of the wave trace of the Aharonov--Bohm Hamiltonian on ${\mathbf{R}}^2$ with multiple solenoids under a generic assumption that no three solenoids are collinear. Then we apply our formula to get a lower bound of scattering resonances in a logarithmic neighborhood near the real axis.

v2: 32 pages, 5 figures. Comments are welcome

References in corpus (3)

• Non-integer valued winding numbers and a generalized Residue Theorem
• Scattering resonances on truncated cones
• The wave trace and resonances of the magnetic Hamiltonian with singular vector potentials

Cited by in corpus (3)

• Schrödinger operators with multiple Aharonov-Bohm fluxes
• The wave trace and resonances of the magnetic Hamiltonian with singular vector potentials
• Resolvent estimates for the magnetic Hamiltonian with singular vector potentials and applications