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

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.

preprint2021arXivOpen access
Mengxuan Yang
math.APmath-phmath.MPmath.SP
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Mengxuan Yang

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