 
Summary: AharonovBohm Effect in Resonances of
Magnetic Schr¨odinger Operators with
Potentials with Supports at Large Separation
Ivana Alexandrova
Department of Mathematics, East Carolina University
124 Austin Building, Greenville, NC 27858, USA
and
Hideo Tamura
Department of Mathematics, Okayama University
Okayama, 7008530, Japan
Abstract
Vector potentials are known to have a direct significance to quantum
particles moving in the magnetic field. This is called the AharonovBohm
effect and is known as one of the most remarkable quantum phenomena.
Here we study this quantum effect through the resonance problem. We
consider the scattering system consisting of two scalar potentials and one
magnetic field with supports at large separation in two dimensions. The
system has trajectories oscillating between these supports. We give a sharp
lower bound on the resonance widths as the distances between the three
supports go to infinity. The bound is described in terms of the backward
