Scattering theory and the Aharonov--Bohm effect in quasiclassical physics

Abstract: Scattering of a nonrelativistic quantum-mechanical particle by an impenetrable magnetic vortex is considered. The nonvanishing transverse size of the vortex is taken into account, and the limit of short, as compared to this size, wavelengths of the scattered particle is analyzed. We show that the scattering Aharonov-Bohm effect persists in the quasiclassical limit owing to the diffraction persisting in the short-wavelength limit. As a result, the vortex flux serves as a gate for the propagation of short-wavelength, almost classical, particles. This quasiclassical effect is more feasible to experimental detection in the case when space outside the vortex is conical.