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Internal control of the Schr\"odinger equation

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Paper breakdownThe authors' claims, conditions and measurements, as JSON Signed receiptProof this review has not been altered
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Camille Laurent (LJLL)

Analysis of PDEs · Submitted 8 Jul 2013

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

The authors' main claim After presenting the basic properties of the equation, we give a self contained proof of the controllability in dimension 1 using some propagation results.

how it is stated · asserted 1.00 read the record →

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arXiv ID1307.2220 (version 1)
Pith IDPUPAFF5N, Pith's permanent record of this paper and its review
CitationCamille Laurent (LJLL). "Internal control of the Schr\"odinger equation." arXiv:1307.2220 (2013). https://pith.science/paper/PUPAFF5N
Claim paper

The compiled record

The paper's own sentences, arranged. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

Open the compiled record

Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 4,791 input tokens, $0.0002 reported.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.35 · human participants 0.02 · controlled comparison 0.06 · randomized assignment 0.01 · states quantitative result 0.04 · compares with prior results 0.31 · mentions code or data availability 0.01.

The abstract, sentence by sentence

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

In this paper, we intend to present some already known results about the internal controllability of the linear and nonlinear Schr\"odinger equation. After presenting the basic properties of the equation, we give a self contained proof of the controllability in dimension 1 using some propagation results. We then discuss how to obtain some similar results on a compact manifold where the zone of control satisfies the Geometric Control Condition. We also discuss some known results and open questions when this condition is not satisfied. Then, we present the links between the controllability and some resolvent estimates. Finally, we discuss the new difficulties when we consider the Nonlinear Schr\"odinger equation.

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 In this paper, we intend to present some already known results about the internal controllability of the linear and nonlinear Schr\"odinger equation. background 0.67 0.14 0.10 asserted 0.75
s1 After presenting the basic properties of the equation, we give a self contained proof of the controllability in dimension 1 using some propagation results. contribution 0.73 0.86 0.14 asserted 1.00
s2 We then discuss how to obtain some similar results on a compact manifold where the zone of control satisfies the Geometric Control Condition. contribution 0.69 0.39 0.07 asserted 0.62
s3 We also discuss some known results and open questions when this condition is not satisfied. background 0.68 0.13 0.04 asserted 0.64
s4 Then, we present the links between the controllability and some resolvent estimates. contribution 0.79 0.25 0.07 asserted 0.94
s5 Finally, we discuss the new difficulties when we consider the Nonlinear Schr\"odinger equation. contribution 0.70 0.25 0.08 asserted 0.73

What kind of paper the classifier reports this is: review 0.80 · evidence from proof or derivation 0.85.

What was examined, and what was not

sources read
  • arXiv listing abstract v1
not examined
  • full text
  • figures and tables
  • references and citing sentences
  • relations to other papers
levels run
  • P abstract
not run
  • S sections
  • T body sentences
  • C citations
  • R cross-paper relations

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

In this paper, we intend to present some already known results about the internal controllability of the linear and nonlinear Schr\"odinger equation. After presenting the basic properties of the equation, we give a self contained proof of the controllability in dimension 1 using some propagation results. We then discuss how to obtain some similar results on a compact manifold where the zone of control satisfies the Geometric Control Condition. We also discuss some known results and open questions when this condition is not satisfied. Then, we present the links between the controllability and some resolvent estimates. Finally, we discuss the new difficulties when we consider the Nonlinear Schr\"odinger equation.

Human review

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How the literature uses it

What this paper does with the arXiv papers it cites

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

What it cites · 2 sentences without a confident label

Cites as background 1 paper

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