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Journal of Physics A Mathematical and General

Aharonov-Bohm scattering on two antiparallel flux lines of the same magnitude-without return flux

Gu Zhi-Yu, Qian Shang-Wu

Published Sep 7, 1993• 2 citations
Publisher

Abstract

The problem of Aharonov-Bohm (AB) scattering on two parallel flux lines of arbitrary magnitude is solved exactly; the expression for the scattering cross-section in the region of geometric shadow is derived. It is shown that in the particular case of two antiparallel lines of the same magnetic flux, though the return flux does not exist, the AB scattering still exists.

DOI
10.1088/0305-4470/26/17/048

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Progress of Theoretical Physics•May 1, 1982•10 citations
The problem of Aharonov-Bohm (AB) scattering on two parallel flux lines of arbitrary magnitude is solved exactly; the expression for the scattering cross-section in the region of geometric shadow is derived. It is shown that in the particular case of two antiparallel lines of the same magnetic flux, though the return flux does not exist, the AB scattering still exists.
The controversial question of the transverse force exerted by the Aharonov-Bohm (AB) magnetic-flux line is reconsidered with the help of a new paraxial solution to the AB-scattering problem. It is shown that despite the left-right symmetry in the AB scattering cross-section, a beam of finite width is deflected by the AB-line as if by the “Lorentz” force. The asymmetry and the magnetic force originate from the quantum interference in the forward direction within the angular size of the incident wave.
The Aharonov-Bohm (AB) equation is reformulated by means of the gauge transformation. A scattering theoretical approach yields an integral equation of the form of Kirchhoff-Huygens. The method to solve this equation is analogous to the one previously used to study the dislocation mediated AB effect. It is reconfirmed that the shadow of the magnetic-flux filament appears in the down stream of the electronic flux. Expression for the large angle scattering obtained by AB is improved and the present expression is shown to agree with numerical solution.