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Nonlinear time-dependent one-dimensional Schroedinger equation with double well potential

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Andrea Sacchetti

Mathematical Physics · Submitted 5 Dec 2002

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

The authors' main claim By means of this stability result we are able to prove the destruction of the beating motion for large enough nonlinearity.

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arXiv IDmath-ph/0212024 (version 1)
Pith ID45NA7U33, Pith's permanent record of this paper and its review
CitationAndrea Sacchetti. "Nonlinear time-dependent one-dimensional Schroedinger equation with double well potential." arXiv:math-ph/0212024 (2002). https://pith.science/paper/45NA7U33
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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 3,002 input tokens.

What the abstract itself states, as probabilities: claims first 0.02 · states limitation 0.63 · human participants 0.01 · controlled comparison 0.04 · randomized assignment 0.01 · states quantitative result 0.25 · compares with prior results 0.08 · mentions code or data availability 0.01.

The abstract, sentence by sentence

arXiv listing abstract v1. Results and the main claim are underlined; .

We consider time-dependent Schroedinger equations in one dimension with double well potential and an external nonlinear perturbation. If the initial state belongs to the eigenspace spanned by the eigenvectors associated to the two lowest eigenvalues then, in the semiclassical limit, we show that the reduction of the time-dependent equation to a 2-mode equation gives the dominant term of the solution with a precise estimate of the error. By means of this stability result we are able to prove the destruction of the beating motion for large enough nonlinearity.

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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 consider time-dependent Schroedinger equations in one dimension with double well potential and an external nonlinear perturbation. background 0.59 0.56 0.03 asserted 0.72
s1 If the initial state belongs to the eigenspace spanned by the eigenvectors associated to the two lowest eigenvalues then, in the semiclassical limit, we show that the reduction of the time-dependent equation to a 2-mode equation gives the dominant term of the solution with a precise estimate of the error. result 0.91 0.94 0.20 asserted 1.00
s2 By means of this stability result we are able to prove the destruction of the beating motion for large enough nonlinearity. result 0.96 0.93 0.67 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 consider time-dependent Schroedinger equations in one dimension with double well potential and an external nonlinear perturbation. If the initial state belongs to the eigenspace spanned by the eigenvectors associated to the two lowest eigenvalues then, in the semiclassical limit, we show that the reduction of the time-dependent equation to a 2-mode equation gives the dominant term of the solution with a precise estimate of the error. By means of this stability result we are able to prove the destruction of the beating motion for large enough nonlinearity.

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