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∈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.
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Citation
Nenciu, G., Richman, E.Sparber, C. (2024). Effective Dynamics of Translationally Invariant Magnetic Schrödinger Equations in the High Field Limit. Annales Henri Poincaré, 1-27. https://doi.org/10.1007/s00023-024-01493-4