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Statistical properties of energy levels of chaotic systems: Wigner or non-Wigner

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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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Jakub Zakrzewski, Karine Dupret, Dominique Delande (Laboratoire Kastler Brossel ENS, Paris, France)

chao-dyn · Submitted 29 Jan 1995

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

The authors' main claim We present here two counterexamples - the hydrogen atom in a magnetic field and the quartic oscillator - which display nearest neighbor statistics strongly different from the usual Wigner distribution.

how it is stated · asserted 1.00 read the record →

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arXiv IDchao-dyn/9501016 (version 1)
Pith IDTU7V5LST, Pith's permanent record of this paper and its review
CitationDominique Delande (Laboratoire Kastler Brossel ENS, France), Jakub Zakrzewski, Karine Dupret, Paris. "Statistical properties of energy levels of chaotic systems: Wigner or non-Wigner." arXiv:chao-dyn/9501016 (1995). https://pith.science/paper/TU7V5LST
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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, 2,945 input tokens, $0.0001 reported.

What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.18 · human participants 0.01 · controlled comparison 0.20 · randomized assignment 0.02 · states quantitative result 0.17 · compares with prior results 0.87 · mentions code or data availability 0.02.

The abstract, sentence by sentence

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

For systems whose classical dynamics is chaotic, it is generally believed that the local statistical properties of the quantum energy levels are well described by Random Matrix Theory. We present here two counterexamples - the hydrogen atom in a magnetic field and the quartic oscillator - which display nearest neighbor statistics strongly different from the usual Wigner distribution. We interpret the results with a simple model using a set of regular states coupled to a set of chaotic states modeled by a random matrix.

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 For systems whose classical dynamics is chaotic, it is generally believed that the local statistical properties of the quantum energy levels are well described by Random Matrix Theory. background 1.00 0.03 0.04 asserted 0.51
s1 We present here two counterexamples - the hydrogen atom in a magnetic field and the quartic oscillator - which display nearest neighbor statistics strongly different from the usual Wigner distribution. result 0.85 0.92 0.73 asserted 1.00
s2 We interpret the results with a simple model using a set of regular states coupled to a set of chaotic states modeled by a random matrix. interpretation 0.93 0.84 0.26 asserted 0.94

What kind of paper the classifier reports this is: simulation study 0.60 · evidence from simulation or computation 0.95.

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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

For systems whose classical dynamics is chaotic, it is generally believed that the local statistical properties of the quantum energy levels are well described by Random Matrix Theory. We present here two counterexamples - the hydrogen atom in a magnetic field and the quartic oscillator - which display nearest neighbor statistics strongly different from the usual Wigner distribution. We interpret the results with a simple model using a set of regular states coupled to a set of chaotic states modeled by a random matrix.

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1 arXiv paper cite this in 1 sentence

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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