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Large-order Perturbation Theory for a Non-Hermitian PT-symmetric Hamiltonian

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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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Carl M. Bender, Gerald V. Dunne

Quantum Physics · Submitted 16 Dec 1998

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

The authors' main claim The analyticity properties of this Stieltjes function lead to a dispersion relation that can be used to compute the imaginary part of the energy for the related real but unstable Hamiltonian $H=p^2+{1/4}x^2-\epsilon x^3$.

how it is stated · asserted 0.96 read the record →

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arXiv IDquant-ph/9812039 (version 1)
Pith IDDPPVRBYZ, Pith's permanent record of this paper and its review
CitationCarl M. Bender, Gerald V. Dunne. "Large-order Perturbation Theory for a Non-Hermitian PT-symmetric Hamiltonian." arXiv:quant-ph/9812039 (1998). https://pith.science/paper/DPPVRBYZ
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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, 4,425 input tokens.

What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.11 · human participants 0.01 · controlled comparison 0.03 · randomized assignment 0.01 · states quantitative result 0.09 · compares with prior results 0.76 · mentions code or data availability 0.02.

The abstract, sentence by sentence

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

A precise calculation of the ground-state energy of the complex PT-symmetric Hamiltonian $H=p^2+{1/4}x^2+i \lambda x^3$, is performed using high-order Rayleigh-Schr\"odinger perturbation theory. The energy spectrum of this Hamiltonian has recently been shown to be real using numerical methods. The Rayleigh-Schr\"odinger perturbation series is Borel summable, and Pad\'e summation provides excellent agreement with the real energy spectrum. Pad\'e analysis provides strong numerical evidence that the once-subtracted ground-state energy considered as a function of $\lambda^2$ is a Stieltjes function. The analyticity properties of this Stieltjes function lead to a dispersion relation that can be used to compute the imaginary part of the energy for the related real but unstable Hamiltonian $H=p^2+{1/4}x^2-\epsilon x^3$.

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 A precise calculation of the ground-state energy of the complex PT-symmetric Hamiltonian $H=p^2+{1/4}x^2+i \lambda x^3$, is performed using high-order Rayleigh-Schr\"odinger perturbation theory. contribution 0.97 0.94 0.18 asserted 1.00
s1 The energy spectrum of this Hamiltonian has recently been shown to be real using numerical methods. background 0.99 0.06 0.05 asserted 1.00
s2 The Rayleigh-Schr\"odinger perturbation series is Borel summable, and Pad\'e summation provides excellent agreement with the real energy spectrum. result 0.92 0.75 0.29 asserted 1.00
s3 Pad\'e analysis provides strong numerical evidence that the once-subtracted ground-state energy considered as a function of $\lambda^2$ is a Stieltjes function. result 0.89 0.83 0.23 asserted 0.81
s4 The analyticity properties of this Stieltjes function lead to a dispersion relation that can be used to compute the imaginary part of the energy for the related real but unstable Hamiltonian $H=p^2+{1/4}x^2-\epsilon x^3$. result 0.37 0.74 0.31 asserted 0.96

What kind of paper the classifier reports this is: theoretical result 0.87 · evidence from simulation or computation 0.95.

What was examined, and what was not

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not examined
  • full text
  • figures and tables
  • references and citing sentences
  • relations to other papers
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  • 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

A precise calculation of the ground-state energy of the complex PT-symmetric Hamiltonian $H=p^2+{1/4}x^2+i \lambda x^3$, is performed using high-order Rayleigh-Schr\"odinger perturbation theory. The energy spectrum of this Hamiltonian has recently been shown to be real using numerical methods. The Rayleigh-Schr\"odinger perturbation series is Borel summable, and Pad\'e summation provides excellent agreement with the real energy spectrum. Pad\'e analysis provides strong numerical evidence that the once-subtracted ground-state energy considered as a function of $\lambda^2$ is a Stieltjes function. The analyticity properties of this Stieltjes function lead to a dispersion relation that can be used to compute the imaginary part of the energy for the related real but unstable Hamiltonian $H=p^2+{1/4}x^2-\epsilon x^3$.

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2 arXiv papers cite this in 5 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

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