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Non existence of vortices in the small density region of a condensate

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Amandine Aftalion, Robert L. Jerrard, Jimena Royo-Letelier

Mathematical Physics · Submitted 27 Aug 2010

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

The authors' main claim In this paper, we answer a question raised by Len Pitaevskii and prove that the ground state of the Gross-Pitaevskii energy describing a Bose Einstein condensate at low rotation does not have vortices in the low density region.

how it is stated · asserted 1.00 read the record →

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arXiv ID1008.4801 (version 2)
Pith IDB7CQT7AQ, Pith's permanent record of this paper and its review
CitationAmandine Aftalion, Jimena Royo-Letelier, Robert L. Jerrard. "Non existence of vortices in the small density region of a condensate." arXiv:1008.4801 (2010). https://pith.science/paper/B7CQT7AQ
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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.

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Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 3,567 input tokens, $0.0001 reported.

What the abstract itself states, as probabilities: claims first 0.11 · states limitation 0.38 · human participants 0.01 · controlled comparison 0.18 · randomized assignment 0.01 · states quantitative result 0.14 · compares with prior results 0.27 · mentions code or data availability 0.01.

The abstract, sentence by sentence

arXiv listing abstract v2. Results and the main claim are underlined; .

In this paper, we answer a question raised by Len Pitaevskii and prove that the ground state of the Gross-Pitaevskii energy describing a Bose Einstein condensate at low rotation does not have vortices in the low density region. Therefore, the first ground state with vortices has its vortices in the bulk. This is obtained by proving that for small rotational velocities, the ground state is multiple of the ground state with zero rotation. We rely on sharp bounds of the decay of the wave function combined with weighted jacobian estimates.

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 answer a question raised by Len Pitaevskii and prove that the ground state of the Gross-Pitaevskii energy describing a Bose Einstein condensate at low rotation does not have vortices in the low density region. result 0.62 0.93 0.92 asserted 1.00
s1 Therefore, the first ground state with vortices has its vortices in the bulk. interpretation 0.73 0.79 0.30 asserted 1.00
s2 This is obtained by proving that for small rotational velocities, the ground state is multiple of the ground state with zero rotation. result 0.63 0.90 0.10 asserted 1.00
s3 We rely on sharp bounds of the decay of the wave function combined with weighted jacobian estimates. method 1.00 0.88 0.03 asserted 0.97

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

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  • arXiv listing abstract v2
not examined
  • full text
  • figures and tables
  • references and citing sentences
  • relations to other papers
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  • 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 answer a question raised by Len Pitaevskii and prove that the ground state of the Gross-Pitaevskii energy describing a Bose Einstein condensate at low rotation does not have vortices in the low density region. Therefore, the first ground state with vortices has its vortices in the bulk. This is obtained by proving that for small rotational velocities, the ground state is multiple of the ground state with zero rotation. We rely on sharp bounds of the decay of the wave function combined with weighted jacobian estimates.

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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

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