Hiroshi T. Ito

Aharonov-Bohm Effect in Scattering by Point-like Magnetic Fields at Large Separation

Abstract. The aim is to study the Aharonov-Bohm effect in the scattering by two point-like magnetic fields at large separation in two dimensions. We analyze the asymptotic behavior of scattering amplitude when the distance between the centers of two fields goes to infinity. The obtained result heavily depends on the fluxes of fields and on incident and final directions.

SEMICLASSICAL ANALYSIS FOR MAGNETIC SCATTERING BY TWO SOLENOIDAL FIELDS

That vector potentials have a direct significance to quantum particles moving in magnetic fields is known as the A-B (Aharonov-Bohm) effect. We study scattering by two solenoidal magnetic fields (point-like magnetic fields) in two dimensions and analyze the asymptotic behavior of the scattering amplitude in the semiclassical limit. The corresponding classical mechanical system has a trajectory oscillating between the centers of the two 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 the centers of the fields. In particular, the A-B effect appears strongly when the centers are on an even line.