Effective Dynamics of Translationally Invariant Magnetic Schrödinger Equations in the High Field Limit

Abstract

We study the large field limit in Schrödinger equations with magnetic vector potentials describing translationally invariant B-fields with respect to the z-axis. In a first step, using regular perturbation theory, we derive an approximate description of the solution, provided the initial data are compactly supported in the Fourier variable dual to \(z\in {{\mathbb {R}}}\). The effective dynamics is thereby seen to produce high-frequency oscillations and large magnetic drifts. In a second step, we show, by using the theory of almost invariant subspaces, that this asymptotic description is stable under polynomially bounded perturbations that vanish in the vicinity of the origin.