Some remarks on the two-dimensional optical theorem and Aharonov-Bohm scattering

M. M. Panja, P K Bera, B. Talukdar

M. Wakamatsu

Christopher C. Gerry, Vijay A. Singh

P. Hraskó

R. Németh, József Cserti

We present a unified treatment of the Aharonov-Bohm (AB) effect for two-dimensional multiband electronic systems possessing isotropic band structures. We propose an integral representation of the AB scattering state of an electron scattered by an infinitely thin solenoid. Moreover, we derive the asymptotic form of the AB scattering state and obtain the differential cross section from that. We found a remarkable result, namely, that this cross section is the same for all isotropic systems and agrees with that obtained first by Aharonov and Bohm for spinless free-particle systems. To demonstrate the generality of our theory, we consider several specific multiband systems relevant to condensed matter physics.

Yu. A. Sitenko, N.D. Vlasii

Quantum-mechanical scattering off a magnetic vortex is considered, and the optical theorem is derived. The vortex core is assumed to be impermeable to scattered particles, and its transverse size is taken into account. We show that the scattering Aharonov–Bohm effect is independent of the choice of boundary conditions from the variety of the Robin ones. The behaviour of the scattering amplitude in the forward direction is analysed, and the persistence of the Fraunhofer diffraction in the short-wavelength limit is shown to be crucial for maintaining the optical theorem in the quasiclassical limit.