dorsal/arxiv
View SchemaTheory of Circle Maps and the Problem of One-Dimensional Optical Resonator with a Periodically Moving Wall
| Authors | R. de la Llave, N. Petrov |
|---|---|
| Categories | |
| ArXiv ID | physics/9810016 |
| URL | https://arxiv.org/abs/physics/9810016 |
| DOI | 10.1103/PhysRevE.59.6637 |
| Journal | Phys. Rev. E 59:6 (1999) 6637-6651 |
Abstract
We consider the electromagnetic field in a cavity with a periodically oscillating perfectly reflecting boundary and show that the mathematical theory of circle maps leads to several physical predictions. Notably, well-known results in the theory of circle maps (which we review briefly) imply that there are intervals of parameters where the waves in the cavity get concentrated in wave packets whose energy grows exponentially. Even if these intervals are dense for typical motions of the reflecting boundary, in the complement there is a positive measure set of parameters where the energy remains bounded.
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"abstract": "We consider the electromagnetic field in a cavity with a periodically\noscillating perfectly reflecting boundary and show that the mathematical theory\nof circle maps leads to several physical predictions. Notably, well-known\nresults in the theory of circle maps (which we review briefly) imply that there\nare intervals of parameters where the waves in the cavity get concentrated in\nwave packets whose energy grows exponentially. Even if these intervals are\ndense for typical motions of the reflecting boundary, in the complement there\nis a positive measure set of parameters where the energy remains bounded.",
"arxiv_id": "physics/9810016",
"authors": [
"R. de la Llave",
"N. Petrov"
],
"categories": [
"physics.optics",
"chao-dyn",
"math-ph",
"math.MP",
"nlin.CD"
],
"doi": "10.1103/PhysRevE.59.6637",
"journal_ref": "Phys. Rev. E 59:6 (1999) 6637-6651",
"title": "Theory of Circle Maps and the Problem of One-Dimensional Optical Resonator with a Periodically Moving Wall",
"url": "https://arxiv.org/abs/physics/9810016"
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