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Rate of Convergence towards Hartree Dynamics with Singular Interaction Potential

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Li Chen, Ji Oon Lee, Jinyeop Lee

Mathematical Physics · Submitted 24 Aug 2017

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

The authors' main claim We show that, with $H^1(\mathbb{R}^3)$ initial data, the difference between the many-body Schr\"odinger evolution in the mean-field regime and the corresponding Hartree dynamics is of order $1/N$, for any fixed time.

how it is stated · asserted 1.00 read the record →

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arXiv ID1708.07278 (version 4)
Pith IDKY4LMTAC, Pith's permanent record of this paper and its review
CitationJinyeop Lee, Ji Oon Lee, Li Chen. "Rate of Convergence towards Hartree Dynamics with Singular Interaction Potential." arXiv:1708.07278 (2017). https://pith.science/paper/KY4LMTAC
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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, 3,028 input tokens.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.49 · human participants 0.01 · controlled comparison 0.23 · randomized assignment 0.01 · states quantitative result 0.97 · compares with prior results 0.21 · mentions code or data availability 0.01.

The abstract, sentence by sentence

arXiv listing abstract v4. Results and the main claim are underlined; .

We consider a system of $N$-Bosons with a two-body interaction potential $V \in L^2(\mathbb{R}^3)+L^\infty(\mathbb{R}^3)$, possibly singular than the Coulomb interaction. We show that, with $H^1(\mathbb{R}^3)$ initial data, the difference between the many-body Schr\"odinger evolution in the mean-field regime and the corresponding Hartree dynamics is of order $1/N$, for any fixed time. The $N$-dependence of the bound is optimal.

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 a system of $N$-Bosons with a two-body interaction potential $V \in L^2(\mathbb{R}^3)+L^\infty(\mathbb{R}^3)$, possibly singular than the Coulomb interaction. background 0.84 0.24 0.03 asserted 0.74
s1 We show that, with $H^1(\mathbb{R}^3)$ initial data, the difference between the many-body Schr\"odinger evolution in the mean-field regime and the corresponding Hartree dynamics is of order $1/N$, for any fixed time. result 0.99 0.96 0.92 asserted 1.00
s2 The $N$-dependence of the bound is optimal. interpretation 0.61 0.79 0.12 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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  • references and citing sentences
  • relations to other papers
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  • P abstract
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  • C citations
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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 a system of $N$-Bosons with a two-body interaction potential $V \in L^2(\mathbb{R}^3)+L^\infty(\mathbb{R}^3)$, possibly singular than the Coulomb interaction. We show that, with $H^1(\mathbb{R}^3)$ initial data, the difference between the many-body Schr\"odinger evolution in the mean-field regime and the corresponding Hartree dynamics is of order $1/N$, for any fixed time. The $N$-dependence of the bound is optimal.

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1 arXiv paper cite this in 4 sentences

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

Papers whose main result relates to this one's

Found among the papers closest to this one by title and main claim. Pith's classifier compared each pair's main results and a second model family confirmed the relation; checked against two further families, shown conflicts agreed 118 times in 120 and shown same results 218 times in 239. The quoted sentence is the other paper's main claim.

States the same result 1 paper
  • We show that the difference between the many-body Schr\"odinger evolution in the mean-field regime and the effective nonlinear Hartree dynamics is at most of the order 1/N, for any fixed time.

    Rate of Convergence Towards Hartree Dynamics · 0.93

Papers citing it · 3 sentences without a confident label

Compares with it 1 paper
  • In particular, the above mentioned integral can be bounded via [equation] Whereas [ref] use the above decomposition of the interaction potential together with Strichartz estimates to control more singular potentials, we want to employ the fact that $|·|^-γ∈L^3/γ_w(^3)$ together with Strichartz estimates both for considering more singular potentials and lowering the required regularity on the initial datum $_0$.

    Convergence rate towards the fractional Hartree-equation with singular potentials in higher Sobolev norms · Preliminary tools and notations · 0.80

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