Quantum scattering in a periodically pulsed magnetic field (Spectral and Scattering Theory and Related Topics)

Abstract

We study the quantum dynamics of a charged particle in the plane in the presence of a periodically pulsed magnetic field perpendicular to the plane. We show that by controlling the cycle when the magnetic field is switched on and off appropriately, the result of the asymptotic completeness of wave operators can be obtained under the assumption that the potential V satisfies the decaying condition |V(x)|leq C(1+|x|)^{- $rho$} for some $rho$>0 . The purpose of this article is to explain the reason why we can admit such a very weak decaying condition.