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

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posted on 2025-02-03, 14:45 authored by Gheorghe Nenciu, Evelyn Richman, Christof SparberChristof Sparber
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.

History

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

Publisher

Springer Nature

Language

  • en

issn

1424-0637