Effective Dynamics of Translationally Invariant Magnetic Schrödinger Equations in the High Field Limit
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2022
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| author | Nenciu, Gheorghe Richman, Evelyn Sparber, Christof |
| author_facet | Nenciu, Gheorghe Richman, Evelyn Sparber, Christof |
| contents | 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 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2208_07894 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Effective Dynamics of Translationally Invariant Magnetic Schrödinger Equations in the High Field Limit Nenciu, Gheorghe Richman, Evelyn Sparber, Christof Mathematical Physics Analysis of PDEs 81Q15 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 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. |
| title | Effective Dynamics of Translationally Invariant Magnetic Schrödinger Equations in the High Field Limit |
| topic | Mathematical Physics Analysis of PDEs 81Q15 |
| url | https://arxiv.org/abs/2208.07894 |