Christof Sparber
University of Illinois Chicago, Chicago, USA

We study the large field limit in Schrödinger equations with magnetic vector potentials describing translationally invariant $B$-fields with respect to the $z$-axis. Using analytic perturbation theory, we derive an approximate description of the solution, provided the initial data is compactly supported in the Fourier-variable dual to $z$. The effective dynamics is thereby seen to produce high-frequency oscillations and large magnetic drifts.

In a second step we show that this asymptotic description is stable under a fairly general class of singular perturbations by using the theory of almost invariant subspaces. This is joint work together with Gheorghe Nenciu and Evelyn Richman.