Stiff three-frequency orbit of the hydrogen atom

Jayme De Luca

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Stiff three-frequency orbit of the hydrogen atom

Jayme De Luca

Atomic Physics · Submitted 21 Nov 2005

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

The authors' main claim This dynamics displays many qualitative agreements with quantum electrodynamics (QED); (i) the unperturbed frequency of each resonant orbit agrees with a corresponding emission line of QED within a few percent on average (ii) the unperturbed orbital frequency of a resonant orbit is given by a difference of two linear eigenvalues (the frequencies of the mutually orthogonal fast modes) and (iii) the averaged angular momentum of gyration is of the order of Planck's constant.

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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, 7,003 input tokens.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.25 · human participants 0.01 · controlled comparison 0.05 · randomized assignment 0.01 · states quantitative result 0.85 · compares with prior results 0.79 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v3. Results and the main claim are underlined; show every role.

We study a stiff quasi-periodic orbit of the electromagnetic two-body problem of Dirac's electrodynamics of point charges. We expand the delay equations of motion about circular orbits to obtain the variational equations up to nonlinear terms. We study the normal modes of the variational dynamics with period of the order of the time for light to travel the interparticle distance. In the atomic magnitude these are fast frequencies compared to the circular rotation. We construct a quasi-periodic orbit with three frequencies; the frequency of the unperturbed circular rotation (slow) and the two fast frequencies of two mutually orthogonal harmonic modes of the variational dynamics. Poynting's theorem gives a simple mechanism for a beat of two mutually orthogonal fast modes to cancel the radiation of the unperturbed circular motion by interference. This mechanism operates when the two fast frequencies beat at the circular frequency, a no-radiation condition. The resonant orbits turn out to have unperturbed orbital angular momenta that are integer multiples of Planck's constant to a good approximation. This dynamics displays many qualitative agreements with quantum electrodynamics (QED); (i) the unperturbed frequency of each resonant orbit agrees with a corresponding emission line of QED within a few percent on average (ii) the unperturbed orbital frequency of a resonant orbit is given by a difference of two linear eigenvalues (the frequencies of the mutually orthogonal fast modes) and (iii) the averaged angular momentum of gyration is of the order of Planck's constant.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#	sentence	role	the authors' own work	states the main conclusion	strength
s0	We study a stiff quasi-periodic orbit of the electromagnetic two-body problem of Dirac's electrodynamics of point charges.	contribution 0.97	0.90	0.04	asserted 0.77
s1	We expand the delay equations of motion about circular orbits to obtain the variational equations up to nonlinear terms.	method 0.99	0.95	0.02	asserted 0.97
s2	We study the normal modes of the variational dynamics with period of the order of the time for light to travel the interparticle distance.	method 0.52	0.89	0.04	asserted 0.98
s3	In the atomic magnitude these are fast frequencies compared to the circular rotation.	interpretation 0.58	0.68	0.03	asserted 1.00
s4	We construct a quasi-periodic orbit with three frequencies; the frequency of the unperturbed circular rotation (slow) and the two fast frequencies of two mutually orthogonal harmonic modes of the variational dynamics.	contribution 0.81	0.95	0.18	asserted 1.00
s5	Poynting's theorem gives a simple mechanism for a beat of two mutually orthogonal fast modes to cancel the radiation of the unperturbed circular motion by interference.	interpretation 0.55	0.74	0.18	asserted 1.00
s6	This mechanism operates when the two fast frequencies beat at the circular frequency, a no-radiation condition.	result 0.58	0.76	0.17	asserted 0.99
s7	The resonant orbits turn out to have unperturbed orbital angular momenta that are integer multiples of Planck's constant to a good approximation.	result 0.99	0.91	0.19	asserted 0.99
s8	This dynamics displays many qualitative agreements with quantum electrodynamics (QED); (i) the unperturbed frequency of each resonant orbit agrees with a corresponding emission line of QED within a few percent on average (ii) the unperturbed orbital frequency of a resonant orbit is given by a difference of two linear eigenvalues (the frequencies of the mutually orthogonal fast modes) and (iii) the averaged angular momentum of gyration is of the order of Planck's constant.	interpretation 0.60	0.84	0.60	asserted 0.97

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

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arXiv listing abstract v3

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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

We study a stiff quasi-periodic orbit of the electromagnetic two-body problem of Dirac's electrodynamics of point charges. We expand the delay equations of motion about circular orbits to obtain the variational equations up to nonlinear terms. We study the normal modes of the variational dynamics with period of the order of the time for light to travel the interparticle distance. In the atomic magnitude these are fast frequencies compared to the circular rotation. We construct a quasi-periodic orbit with three frequencies; the frequency of the unperturbed circular rotation (slow) and the two fast frequencies of two mutually orthogonal harmonic modes of the variational dynamics. Poynting's theorem gives a simple mechanism for a beat of two mutually orthogonal fast modes to cancel the radiation of the unperturbed circular motion by interference. This mechanism operates when the two fast frequencies beat at the circular frequency, a no-radiation condition. The resonant orbits turn out to have unperturbed orbital angular momenta that are integer multiples of Planck's constant to a good approximation. This dynamics displays many qualitative agreements with quantum electrodynamics (QED); (i) the unperturbed frequency of each resonant orbit agrees with a corresponding emission line of QED within a few percent on average (ii) the unperturbed orbital frequency of a resonant orbit is given by a difference of two linear eigenvalues (the frequencies of the mutually orthogonal fast modes) and (iii) the averaged angular momentum of gyration is of the order of Planck's constant.

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