On the scattering Aharonov–Bohm effect. (21st March 2019) - Ivetić, Boris
Abstract: In this paper we review some aspects of the scattering Aharonov–Bohm effect and Berry's phase. Specifically, the problem of scattering of free 2d electrons on the system of an arbitrary number of parallel, infinitely thin and infinitely long coils (non-interacting, point magnetic fluxes) is modeled as free semi-classical particle propagation on a topologically non-trivial background. We show that in this case it is possible to obtain Berry's phase by integration. First the case of a single coil is analyzed, upon which a particular solution for the case of scattering on an arbitrary number of coils is found. Considering the solution in the momentum representation, an analytic continuation of the angle coordinate in the momentum space is introduced, in accord with the non-trivial geometry of the configuration space. Finally, some simple experiments with possible applications for quantum computing are proposed.