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Rigorous Derivation of the Gross-Pitaevskii Equation

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Laszlo Erdos, Benjamin Schlein, Horng-Tzer Yau

Mathematical Physics · Submitted 10 Dec 2006

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

The authors' main claim We present a rigorous proof of this fact starting from a many-body bosonic Schroedinger equation with a short scale repulsive interaction in the dilute limit.

how it is stated · asserted 1.00 read the record →

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arXiv IDmath-ph/0612028 (version 1)
Pith ID6JB2P7I3, Pith's permanent record of this paper and its review
CitationBenjamin Schlein, Horng-Tzer Yau, Laszlo Erdos. "Rigorous Derivation of the Gross-Pitaevskii Equation." arXiv:math-ph/0612028 (2006). https://pith.science/paper/6JB2P7I3
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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, 2,889 input tokens.

What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.19 · human participants 0.01 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.04 · compares with prior results 0.06 · mentions code or data availability 0.02.

The abstract, sentence by sentence

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

The time dependent Gross-Pitaevskii equation describes the dynamics of initially trapped Bose-Einstein condensates. We present a rigorous proof of this fact starting from a many-body bosonic Schroedinger equation with a short scale repulsive interaction in the dilute limit. Our proof shows the persistence of an explicit short scale correlation structure in the condensate.

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 The time dependent Gross-Pitaevskii equation describes the dynamics of initially trapped Bose-Einstein condensates. background 1.00 0.06 0.10 asserted 1.00
s1 We present a rigorous proof of this fact starting from a many-body bosonic Schroedinger equation with a short scale repulsive interaction in the dilute limit. contribution 0.91 0.95 0.48 asserted 1.00
s2 Our proof shows the persistence of an explicit short scale correlation structure in the condensate. result 0.98 0.94 0.25 asserted 1.00

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

What was examined, and what was not

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  • arXiv listing abstract v1
not examined
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  • figures and tables
  • references and citing sentences
  • relations to other papers
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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

The time dependent Gross-Pitaevskii equation describes the dynamics of initially trapped Bose-Einstein condensates. We present a rigorous proof of this fact starting from a many-body bosonic Schroedinger equation with a short scale repulsive interaction in the dilute limit. Our proof shows the persistence of an explicit short scale correlation structure in the condensate.

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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
  • Starting from many body quantum dynamics, we present a rigorous derivation of a cubic nonlinear Schroedinger equation known as the Gross-Pitaevskii equation for the time evolution of the condensate wave function.

    Dynamics of Bose-Einstein Condensates · 0.98

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