两个通量相反的Aharonov-Bohm涡旋的散射
Scattering on two Aharonov-Bohm vortices with opposite fluxes
摘要：
详细研究了入射平面波在两个磁通量相反的Aharonov-Bohm涡旋上的散射。涡的存在施加非平凡的边界条件的切割连接两个涡的分波。这些条件导致入射和出射分波之间的散射振幅的无限方程组，其可以数值求解。本文的重点是在小通量极限和小涡分离极限两种极限下散射振幅的解析确定。在后者的限制，主要贡献来自S波振幅。然而，计算它仍然需要求解一个无限的方程组，这是通过黎曼-希尔伯特方法实现的。计算结果与数值计算结果吻合较好。
英文摘要：
The scattering of an incident plane wave on two Aharonov-Bohm vortices with opposite fluxes is considered in detail. The presence of the vortices imposes non-trivial boundary conditions for the partial waves on a cut joining the two vortices. These conditions result in an infinite system of equations for scattering amplitudes between incoming and outgoing partial waves, which can be solved numerically. The main focus of the paper is the analytic determination of the scattering amplitude in two limits, the small flux limit and the limit of small vortex separation. In the latter limit the dominant contribution comes from the S-wave amplitude. Calculating it, however, still requires solving an infinite system of equations, which is achieved by the Riemann-Hilbert method. The results agree well with the numerical calculations.
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