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

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Gheorghe Nenciu, Evelyn Richman, Christof Sparber

Mathematical Physics · Submitted 16 Aug 2022

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim 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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arXiv ID2208.07894 (version 3)
Pith IDO6EOUDT5, Pith's permanent record of this paper and its review
CitationChristof Sparber, Evelyn Richman, Gheorghe Nenciu. "Effective Dynamics of Translationally Invariant Magnetic Schr\"odinger Equations in the High Field Limit." arXiv:2208.07894 (2022). https://pith.science/paper/O6EOUDT5
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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 3,674 input tokens.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.86 · human participants 0.01 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.06 · compares with prior results 0.05 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v3. Results and the main claim are underlined; .

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.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 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. contribution 0.86 0.87 0.06 asserted 0.90
s1 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 $z\in \mathbb R$. method 0.81 0.95 0.08 asserted 0.99
s2 The effective dynamics is thereby seen to produce high-frequency oscillations and large magnetic drifts. result 0.74 0.88 0.36 asserted 0.99
s3 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. result 0.59 0.94 0.33 asserted 1.00

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 1.00.

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Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper
Original 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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