English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

We study the large field limit in Schr\"odinger equations with magneticvector potentials describing translationally invariant $B$-fields with respectto the $z$-axis. Using analytic perturbation theory, we derive an approximatedescription of the solution, provided the initial data is compactly supportedin the Fourier-variable dual to $z\in \mathbb{R}$. The effective dynamics isthereby seen to produce high-frequency oscillations and large magnetic drifts.In a second step we show that this asymptotic description is stable under afairly general class of singular perturbations by using the theory of almostinvariant subspaces. To this end, we also give an elementary proof of theexponential decay of the resolvent and the eigenfunctions of confiningSchr\"odinger operators.

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