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Exponential Decay and Ionization Thresholds in Non-Relativistic Quantum Electrodynamics

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Marcel Griesemer

Mathematical Physics · Submitted 17 Jun 2002

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

The authors' main claim We show that these two definitions agree, and that the electrons described by a state with energy below the ionization threshold are localized in a small neighborhood of the nuclei with a probability that approaches 1 exponentially fast with increasing radius of the neighborhood.

how it is stated · asserted 1.00 read the record →

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arXiv IDmath-ph/0206024 (version 2)
Pith IDJRLNKM2N, Pith's permanent record of this paper and its review
CitationMarcel Griesemer. "Exponential Decay and Ionization Thresholds in Non-Relativistic Quantum Electrodynamics." arXiv:math-ph/0206024 (2002). https://pith.science/paper/JRLNKM2N
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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, 4,269 input tokens.

What the abstract itself states, as probabilities: claims first 0.05 · states limitation 0.14 · human participants 0.01 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.43 · compares with prior results 0.12 · mentions code or data availability 0.01.

The abstract, sentence by sentence

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

Spatial localization of the electrons of an atom or molecule is studied in models of non-relativistic matter coupled to quantized radiation. We give two definitions of the ionization threshold. One in terms of spectral data of cluster Hamiltonians, and one in terms of minimal energies of non-localized states. We show that these two definitions agree, and that the electrons described by a state with energy below the ionization threshold are localized in a small neighborhood of the nuclei with a probability that approaches 1 exponentially fast with increasing radius of the neighborhood. The latter result is derived from a new, general result on exponential decay tailored to fit our problem, but applicable to many non-relativistic quantum systems outside quantum electrodynamics as well.

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 Spatial localization of the electrons of an atom or molecule is studied in models of non-relativistic matter coupled to quantized radiation. background 0.71 0.56 0.03 asserted 0.88
s1 We give two definitions of the ionization threshold. contribution 0.96 0.94 0.03 asserted 0.98
s2 One in terms of spectral data of cluster Hamiltonians, and one in terms of minimal energies of non-localized states. contribution 0.69 0.84 0.05 asserted 0.84
s3 We show that these two definitions agree, and that the electrons described by a state with energy below the ionization threshold are localized in a small neighborhood of the nuclei with a probability that approaches 1 exponentially fast with increasing radius of the neighborhood. result 1.00 0.96 0.87 asserted 1.00
s4 The latter result is derived from a new, general result on exponential decay tailored to fit our problem, but applicable to many non-relativistic quantum systems outside quantum electrodynamics as well. method 0.58 0.92 0.15 asserted 1.00

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

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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

Spatial localization of the electrons of an atom or molecule is studied in models of non-relativistic matter coupled to quantized radiation. We give two definitions of the ionization threshold. One in terms of spectral data of cluster Hamiltonians, and one in terms of minimal energies of non-localized states. We show that these two definitions agree, and that the electrons described by a state with energy below the ionization threshold are localized in a small neighborhood of the nuclei with a probability that approaches 1 exponentially fast with increasing radius of the neighborhood. The latter result is derived from a new, general result on exponential decay tailored to fit our problem, but applicable to many non-relativistic quantum systems outside quantum electrodynamics as well.

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References
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1 arXiv paper 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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