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Periodic orbit action correlations in the Baker map

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Gregor Tanner

Chaotic Dynamics · Submitted 13 Jan 2000

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

The authors' main claim Periodic orbit correlations are found to agree quantitatively with the predictions from random matrix theory up to a critical length determined by the semiclassical error.

how it is stated · asserted 1.00 read the record →

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arXiv IDnlin/0001024 (version 1)
Pith IDXBCU5EEQ, Pith's permanent record of this paper and its review
CitationGregor Tanner. "Periodic orbit action correlations in the Baker map." arXiv:nlin/0001024 (2000). https://pith.science/paper/XBCU5EEQ
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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, 4,873 input tokens.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.88 · human participants 0.01 · controlled comparison 0.16 · randomized assignment 0.01 · states quantitative result 0.68 · compares with prior results 0.82 · mentions code or data availability 0.02.

The abstract, sentence by sentence

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

Periodic orbit action correlations are studied for the piecewise linear, area-preserving Baker map. Semiclassical periodic orbit formulae together with universal spectral statistics in the corresponding quantum Baker map suggest the existence of universal periodic orbit correlations. The calculation of periodic orbit sums for the Baker map can be performed with the help of a Perron-Frobenius type operator. This makes it possible to study periodic orbit correlations for orbits with period up to 500 iterations of the map. Periodic orbit correlations are found to agree quantitatively with the predictions from random matrix theory up to a critical length determined by the semiclassical error. Exponentially increasing terms dominate the correlations for longer orbits which are due to the violation of unitarity in the semiclassical approximation.

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 Periodic orbit action correlations are studied for the piecewise linear, area-preserving Baker map. contribution 0.89 0.81 0.04 asserted 0.93
s1 Semiclassical periodic orbit formulae together with universal spectral statistics in the corresponding quantum Baker map suggest the existence of universal periodic orbit correlations. background 0.89 0.15 0.14 hedged possibility 1.00
s2 The calculation of periodic orbit sums for the Baker map can be performed with the help of a Perron-Frobenius type operator. method 0.99 0.37 0.03 asserted 0.71
s3 This makes it possible to study periodic orbit correlations for orbits with period up to 500 iterations of the map. method 0.92 0.64 0.04 hedged possibility 0.53
s4 Periodic orbit correlations are found to agree quantitatively with the predictions from random matrix theory up to a critical length determined by the semiclassical error. result 1.00 0.90 0.66 asserted 1.00
s5 Exponentially increasing terms dominate the correlations for longer orbits which are due to the violation of unitarity in the semiclassical approximation. result 0.51 0.80 0.23 asserted 1.00

What kind of paper the classifier reports this is: simulation study 0.71 · evidence from simulation or computation 0.98.

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  • S sections
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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

Periodic orbit action correlations are studied for the piecewise linear, area-preserving Baker map. Semiclassical periodic orbit formulae together with universal spectral statistics in the corresponding quantum Baker map suggest the existence of universal periodic orbit correlations. The calculation of periodic orbit sums for the Baker map can be performed with the help of a Perron-Frobenius type operator. This makes it possible to study periodic orbit correlations for orbits with period up to 500 iterations of the map. Periodic orbit correlations are found to agree quantitatively with the predictions from random matrix theory up to a critical length determined by the semiclassical error. Exponentially increasing terms dominate the correlations for longer orbits which are due to the violation of unitarity in the semiclassical approximation.

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