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 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.