Scattering on two Aharonov-Bohm vortices with opposite fluxes - Nonlinear Sciences > Exactly Solvable and Integrable SystemsReport as inadecuate




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Abstract: The scattering of an incident plane wave on two Aharonov-Bohm vortices withopposite fluxes is considered in detail. The presence of the vortices imposesnon-trivial boundary conditions for the partial waves on a cut joining the twovortices. These conditions result in an infinite system of equations forscattering amplitudes between incoming and outgoing partial waves, which can besolved numerically. The main focus of the paper is the analytic determinationof the scattering amplitude in two limits, the small flux limit and the limitof small vortex separation. In the latter limit the dominant contribution comesfrom the S-wave amplitude. Calculating it, however, still requires solving aninfinite system of equations, which is achieved by the Riemann-Hilbert method.The results agree well with the numerical calculations.



Author: E Bogomolny, S Mashkevich, S Ouvry

Source: https://arxiv.org/







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