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arXiv · 2208.07894

Effective Dynamics of Translationally Invariant Magnetic Schr\"odinger Equations in the High Field Limit

Gheorghe Nenciu·Evelyn Richman·Christof Sparber
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Abstract

We study the large field limit in Schr\"odinger 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 is 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.

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Gheorghe Nenciu, Evelyn Richman, Christof Sparber. 2022-08-16. Effective Dynamics of Translationally Invariant Magnetic Schr\"odinger Equations in the High Field Limit. https://arxiv.org/abs/2208.07894

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