Asymptotic behavior of scattering amplitudes in magnetic fields at large separation

Magnetic potentials have a direct significance to the motion of particles in quantum mechanics. This is known as the Aharonov-Bohm effect. We study this quantum property in the scattering by two magnetic fields at large separation in two dimensions. We derive the asymptotic formula of scattering amplitude when the distance between the centers of two fields goes to infinity. The result depends on the fluxes of fields and on incident and final directions. We here consider only the simple case that at least one of two fluxes is zero.