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

宏 伊藤, 英男 田村

Hiroshi T. ITO, Hideo Tamura

Ivana Alexandrova, Hideo Tamura

Bernard Zygelman

Hiroshi T. ITO, Hideo Tamura

According to the Aharonov–Bohm effect, magnetic potentials have a direct significance to the motion of particles in quantum mechanics. We study this quantum effect through the scattering by several point‐like magnetic fields at large separation in two dimensions. We derive the asymptotic formula for scattering amplitudes as the distances between centers of fields go to infinity. The result heavily depends on the location of centers. A special emphasis is placed on the case of scattering by fields with centers on an even line. The obtained formula depends on fluxes of fields and on ratios of distances between adjacent centers. We figure the approximate values of differential cross sections to see how the pattern of interferences changes with flux parameters.

Hideo Tamura

We study the Aharonov–Bohm (AB) effect through resonances for magnetic scattering in two dimensions. The scattering system consists of three scatterers, one bounded obstacle, and two scalar potentials with compact supports at large separation, where the obstacle is placed between two supports and the support of the magnetic field is completely shielded by the obstacle. The field does not influence particles from a classical mechanical point of view, but quantum particles are influenced by the corresponding vector potential which does not necessarily vanish outside the obstacle. This quantum phenomenon is called the AB effect. The resonances are shown to be generated near the real axis by the trajectories oscillating between two supports of the scalar potentials as the distances between the three scatterers go to infinity. The location is described in terms of the backward amplitudes for scattering by each of the scalar potentials and by the obstacle, and it depends heavily on the magnetic flux of the field.