Spectral asymptotic analysis for Schrodinger operators

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We have studied the Aharonov-Bohm effect (AB effect) in resonances through a simple scattering systemin two dimensions. The system consists of three scatterers, one bounded obstacle and two scalar potentials with compact supports at large separation, where the obstacle is placed between two supports and shields completely the support of a magnetic field. We have obtained that the resonances are generated nearthe real axis by the trajectories trapped between two supports of the scalar potentials and that the location depends heavily on the magnetic flux. This clarifies that the AB effect is deeply involved in resonances for magnetic scattering.