Scattering by magnetic fields and Aharonov-Bohm effect

本课题致力于研究二维多个点状磁场的散射问题。根据Aharonov-Bohm效应，在量子力学中，磁势对粒子的运动具有直接意义。我们通过二维大间隔的多个点状磁场的散射来研究这种量子效应。我们推导了当场中心之间的距离趋于无穷大时，散射幅度的渐近公式。特别强调中心在偶数线上的场的散射情况。得到的结果依赖于场的通量和相邻中心之间的距离比。我们计算了由微分截面的渐近公式得到的近似值，我们看到了干涉图案如何随着通量参数的变化而变化。

The present project has been devoted to the study on the scattering problem by several point-like magnetic fields in two dimensions. 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. A special emphasis is placed on the case of scattering by fields with centers on an even line. The obtained result depends on fluxes of fields and on ratios of distances between adjacent centers. We figure the approximate values obtained from the asymptotic formula for the differential cross sections and we see how the pattern of interferences changes with flux parameters.