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arXiv · 2105.06542

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

Mengxuan Yang
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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.

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Mengxuan Yang. 2021-05-13. The wave trace and resonances of the magnetic Hamiltonian with singular vector potentials. https://doi.org/10.1007/s00220-021-04261-1

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