dorsal/arxiv
View SchemaStiff three-frequency orbit of the hydrogen atom
| Authors | Jayme De Luca |
|---|---|
| Categories | |
| ArXiv ID | physics/0511179 |
| URL | https://arxiv.org/abs/physics/0511179 |
| DOI | 10.1103/PhysRevE.73.026221 |
| Journal | The Physical Review E, vol. 73, 026221 (2006) |
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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"abstract": "We study a stiff quasi-periodic orbit of the electromagnetic two-body problem\nof Dirac\u0027s electrodynamics of point charges. We expand the delay equations of\nmotion about circular orbits to obtain the variational equations up to\nnonlinear terms. We study the normal modes of the variational dynamics with\nperiod of the order of the time for light to travel the interparticle distance.\nIn the atomic magnitude these are fast frequencies compared to the circular\nrotation. We construct a quasi-periodic orbit with three frequencies; the\nfrequency of the unperturbed circular rotation (slow) and the two fast\nfrequencies of two mutually orthogonal harmonic modes of the variational\ndynamics. Poynting\u0027s theorem gives a simple mechanism for a beat of two\nmutually orthogonal fast modes to cancel the radiation of the unperturbed\ncircular motion by interference. This mechanism operates when the two fast\nfrequencies beat at the circular frequency, a no-radiation condition. The\nresonant orbits turn out to have unperturbed orbital angular momenta that are\ninteger multiples of Planck\u0027s constant to a good approximation. This dynamics\ndisplays many qualitative agreements with quantum electrodynamics (QED); (i)\nthe unperturbed frequency of each resonant orbit agrees with a corresponding\nemission line of QED within a few percent on average (ii) the unperturbed\norbital frequency of a resonant orbit is given by a difference of two linear\neigenvalues (the frequencies of the mutually orthogonal fast modes) and (iii)\nthe averaged angular momentum of gyration is of the order of Planck\u0027s constant.",
"arxiv_id": "physics/0511179",
"authors": [
"Jayme De Luca"
],
"categories": [
"physics.atom-ph"
],
"doi": "10.1103/PhysRevE.73.026221",
"journal_ref": "The Physical Review E, vol. 73, 026221 (2006)",
"title": "Stiff three-frequency orbit of the hydrogen atom",
"url": "https://arxiv.org/abs/physics/0511179"
},
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