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Decay rates of bound states at the spectral threshold of multi-particle Schr\"odinger operators

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Simon Barth, Andreas Bitter

Mathematical Physics · Submitted 22 Nov 2019

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

The authors' main claim We give the asymptotic behaviour of the corresponding eigenfunction in dependence of the dimension and the number of particles of the system.

how it is stated · asserted 1.00 read the record →

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arXiv ID1911.10061 (version 2)
Pith IDO42RHLFL, Pith's permanent record of this paper and its review
CitationAndreas Bitter, Simon Barth. "Decay rates of bound states at the spectral threshold of multi-particle Schr\"odinger operators." arXiv:1911.10061 (2019). https://pith.science/paper/O42RHLFL
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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-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 2,345 input tokens.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.25 · human participants 0.01 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.15 · compares with prior results 0.04 · mentions code or data availability 0.01.

The abstract, sentence by sentence

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

We consider $N$-body Schr\"odinger operators with $N\geq3$ particles in dimension $d\geq 3$ in the critical case when the lowest eigenvalue coincides with the bottom of the essential spectrum of the operator. We give the asymptotic behaviour of the corresponding eigenfunction in dependence of the dimension and the number of particles of the system.

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 consider $N$-body Schr\"odinger operators with $N\geq3$ particles in dimension $d\geq 3$ in the critical case when the lowest eigenvalue coincides with the bottom of the essential spectrum of the operator. background 0.77 0.26 0.05 asserted 0.80
s1 We give the asymptotic behaviour of the corresponding eigenfunction in dependence of the dimension and the number of particles of the system. result 0.87 0.94 0.82 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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  • P abstract
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  • 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

We consider $N$-body Schr\"odinger operators with $N\geq3$ particles in dimension $d\geq 3$ in the critical case when the lowest eigenvalue coincides with the bottom of the essential spectrum of the operator. We give the asymptotic behaviour of the corresponding eigenfunction in dependence of the dimension and the number of particles of the system.

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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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