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Bohr-Sommerfeld Quantization of Periodic Orbits

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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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Gabor Vattay (Division de Physique Théorique, Institut de Physique Nucléaire, Orsay Cedex, France)

chao-dyn · Submitted 16 Nov 1995

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

The authors' main claim We show, that the canonical invariant part of $\hbar$ corrections to the Gutzwiller trace formula and the Gutzwiller-Voros spectral determinant can be computed by the Bohr-Sommerfeld quantization rules, which usually apply for integrable systems.

how it is stated · asserted 1.00 read the record →

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arXiv IDchao-dyn/9511003 (version 2)
Pith IDVWMESHBE, Pith's permanent record of this paper and its review
CitationFrance), Gabor Vattay (Division de Physique Th\'eorique, Institut de Physique Nucl\'eaire, Orsay cedex. "Bohr-Sommerfeld Quantization of Periodic Orbits." arXiv:chao-dyn/9511003 (1995). https://pith.science/paper/VWMESHBE
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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, 2,947 input tokens, $0.0001 reported.

What the abstract itself states, as probabilities: claims first 0.05 · states limitation 0.12 · human participants 0.01 · controlled comparison 0.12 · randomized assignment 0.01 · states quantitative result 0.07 · compares with prior results 0.81 · mentions code or data availability 0.02.

The abstract, sentence by sentence

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

We show, that the canonical invariant part of $\hbar$ corrections to the Gutzwiller trace formula and the Gutzwiller-Voros spectral determinant can be computed by the Bohr-Sommerfeld quantization rules, which usually apply for integrable systems. We argue that the information content of the classical action and stability can be used more effectively than in the usual treatment. We demonstrate the improvement of precision on the example of the three disk scattering 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 show, that the canonical invariant part of $\hbar$ corrections to the Gutzwiller trace formula and the Gutzwiller-Voros spectral determinant can be computed by the Bohr-Sommerfeld quantization rules, which usually apply for integrable systems. result 0.74 0.93 0.87 asserted 1.00
s1 We argue that the information content of the classical action and stability can be used more effectively than in the usual treatment. contribution 0.48 0.42 0.09 asserted 0.49
s2 We demonstrate the improvement of precision on the example of the three disk scattering system. result 0.65 0.94 0.10 asserted 1.00

What kind of paper the classifier reports this is: theoretical result 0.86 · evidence from proof or derivation 0.55.

What was examined, and what was not

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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
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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 show, that the canonical invariant part of $\hbar$ corrections to the Gutzwiller trace formula and the Gutzwiller-Voros spectral determinant can be computed by the Bohr-Sommerfeld quantization rules, which usually apply for integrable systems. We argue that the information content of the classical action and stability can be used more effectively than in the usual treatment. We demonstrate the improvement of precision on the example of the three disk scattering system.

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