Summary: Resonance Free Regions in Magnetic Scattering
by Two Solenoidal Fields at Large Separation
124 Austin Building, Department of Mathematics
East Carolina University, Greenville, NC 27858, USA
Department of Mathematics, Okayama University
Okayama, 7008530, Japan
We consider the problem of quantum resonances in magnetic scattering by two
solenoidal fields at large separation in two dimensions. This system has trapped tra-
jectories oscillating between two centers of the fields. We give a sharp lower bound
on resonance widths when the distance between the two centers goes to infinity. The
bound is described in terms of backward amplitudes calculated explicitly for scattering
by each solenoidal field. The study is based on a new type of complex scaling method.
As an application, we also discuss the relation to semiclassical resonances in scattering
by two solenoidal fields.
Running Head : Resonances for scattering by solenoidal fields
Keywords : Resonances; magnetic scattering; solenoidal fields; Aharonov-Bohm effect.