Aharonov–Bohm effect in scattering by a chain of point‐like magnetic fields

Article type: Research Article

Authors: Ito, Hiroshi T.^; | Tamura, Hideo

Affiliations: Department of Computer Science, Ehime University, Matsuyama 790‐8577, Japan E‐mail: [email protected]‐u.ac.jp | Department of Mathematics, Okayama University, Okayama 700‐8530, Japan E‐mail: [email protected]‐u.ac.jp

Note: [] Corresponding author.

Abstract: 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.

Journal: Asymptotic Analysis, vol. 34, no. 3-4, pp. 199-240, 2003