dorsal/arxiv
View SchemaStiff Stability of the Hydrogen atom in dissipative Fokker electrodynamics
| Authors | Jayme De Luca |
|---|---|
| Categories | |
| ArXiv ID | physics/0505206 |
| URL | https://arxiv.org/abs/physics/0505206 |
| DOI | 10.1103/PhysRevE.71.056210 |
| Journal | Phys. Rev. E vol. 71, paper 056210, May 2005 |
Abstract
We introduce an ad-hoc electrodynamics with advanced and retarded Lienard-Wiechert interactions plus the dissipative Lorentz-Dirac self-interaction force. We study the covariant dynamical system of the electromagnetic two-body problem, i.e., the hydrogen atom. We perform the linear stability analysis of circular orbits for oscillations perpendicular to the orbital plane. In particular we study the normal modes of the linearized dynamics that have an arbitrarily large imaginary eigenvalue. These large eigenvalues are fast frequencies that introduce a fast (stiff) timescale into the dynamics. As an application, we study the phenomenon of resonant dissipation, i.e., a motion where both particles recoil together in a drifting circular orbit (a bound state), while the atom dissipates center-of-mass energy only. This balancing of the stiff dynamics is established by the existence of a quartic resonant constant that locks the dynamics to the neighborhood of the recoiling circular orbit. The resonance condition quantizes the angular momenta in reasonable agreement with the Bohr atom. The principal result is that the emission lines of quantum electrodynamics (QED) agree with the prediction of our resonance condition within one percent average deviation.
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"abstract": "We introduce an ad-hoc electrodynamics with advanced and retarded\nLienard-Wiechert interactions plus the dissipative Lorentz-Dirac\nself-interaction force. We study the covariant dynamical system of the\nelectromagnetic two-body problem, i.e., the hydrogen atom. We perform the\nlinear stability analysis of circular orbits for oscillations perpendicular to\nthe orbital plane. In particular we study the normal modes of the linearized\ndynamics that have an arbitrarily large imaginary eigenvalue. These large\neigenvalues are fast frequencies that introduce a fast (stiff) timescale into\nthe dynamics. As an application, we study the phenomenon of resonant\ndissipation, i.e., a motion where both particles recoil together in a drifting\ncircular orbit (a bound state), while the atom dissipates center-of-mass energy\nonly. This balancing of the stiff dynamics is established by the existence of a\nquartic resonant constant that locks the dynamics to the neighborhood of the\nrecoiling circular orbit. The resonance condition quantizes the angular momenta\nin reasonable agreement with the Bohr atom. The principal result is that the\nemission lines of quantum electrodynamics (QED) agree with the prediction of\nour resonance condition within one percent average deviation.",
"arxiv_id": "physics/0505206",
"authors": [
"Jayme De Luca"
],
"categories": [
"physics.atom-ph"
],
"doi": "10.1103/PhysRevE.71.056210",
"journal_ref": "Phys. Rev. E vol. 71, paper 056210, May 2005",
"title": "Stiff Stability of the Hydrogen atom in dissipative Fokker electrodynamics",
"url": "https://arxiv.org/abs/physics/0505206"
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