dorsal/arxiv
View SchemaThe critical manifold of the Lorentz-Dirac equation
| Authors | Herbert Spohn |
|---|---|
| Categories | |
| ArXiv ID | physics/9911027 |
| URL | https://arxiv.org/abs/physics/9911027 |
| DOI | 10.1209/epl/i2000-00268-x |
| Journal | Europhys.Lett.49:287-292,2000 |
Abstract
We investigate the solutions to the Lorentz-Dirac equation and show that its solution flow has a structure identical to the one of renormalization group flows in critical phenomena. The physical solutions of the Lorentz-Dirac equation lie on the critical surface. The critical surface is repelling, i.e. any slight deviation from it is amplified and as a result the solution runs away to infinity. On the other hand, Dirac's asymptotic condition (acceleration vanishes for long times) forces the solution to be on the critical manifold. The critical surface can be determined perturbatively. Thereby one obtains an effective second order equation, which we apply to various cases, in particular to the motion of an electron in a Penning trap.
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"abstract": "We investigate the solutions to the Lorentz-Dirac equation and show that its\nsolution flow has a structure identical to the one of renormalization group\nflows in critical phenomena. The physical solutions of the Lorentz-Dirac\nequation lie on the critical surface. The critical surface is repelling, i.e.\nany slight deviation from it is amplified and as a result the solution runs\naway to infinity. On the other hand, Dirac\u0027s asymptotic condition (acceleration\nvanishes for long times) forces the solution to be on the critical manifold.\nThe critical surface can be determined perturbatively. Thereby one obtains an\neffective second order equation, which we apply to various cases, in particular\nto the motion of an electron in a Penning trap.",
"arxiv_id": "physics/9911027",
"authors": [
"Herbert Spohn"
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"doi": "10.1209/epl/i2000-00268-x",
"journal_ref": "Europhys.Lett.49:287-292,2000",
"title": "The critical manifold of the Lorentz-Dirac equation",
"url": "https://arxiv.org/abs/physics/9911027"
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