Hiroshi T. Ito and Hideo Tamura 
Semiclassical analysis for magnetic scattering by two solenoidal fields 
(504K, Postscript)

ABSTRACT.  It is known as the A--B (Aharonov--Bohm) effect that vector potentials have a direct significance to quantum particles moving in magnetic fields. We study the scattering by two solenoidal magnetic fields 
(point--like magnetic fields) in two dimensions and analyze the asymptotic behavior of scattering amplitude in the semiclassical limit. The corresponding classical mechanical system has the trajectory oscillating between two centers of fields. We derive the asymptotic formula with the first three terms and make clear how such a trapping trajectory is reflected in the asymptotic formula through the A--B effect. We also make a brief comment on an extension to the scattering by many solenoidal fields. The result depends on the location of centers of fields. In particular, the A--B effect strongly appears when centers are on an even line.