dorsal/arxiv
View SchemaRegimes of stability of accelerator modes
| Authors | Rebecca Hihinashvili, Tali Oliker, Yaniv S. Avizrats, Alexander Iomin, Shmuel Fishman, Italo Guarneri |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0604006 |
| URL | https://arxiv.org/abs/quant-ph/0604006 |
| DOI | 10.1016/j.physd.2006.10.008 |
Abstract
The phase diagram of a simple area-preserving map, which was motivated by the quantum dynamics of cold atoms, is explored analytically and numerically. Periodic orbits of a given winding ratio are found to exist within wedge-shaped regions in the phase diagrams, which are analogous to the Arnol'd tongues which have been extensively studied for a variety of dynamical systems, mostly dissipative ones. A rich variety of bifurcations of various types are observed, as well as period doubling cascades. Stability of periodic orbits is analyzed in detail.
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"abstract": "The phase diagram of a simple area-preserving map, which was motivated by the\nquantum dynamics of cold atoms, is explored analytically and numerically.\nPeriodic orbits of a given winding ratio are found to exist within wedge-shaped\nregions in the phase diagrams, which are analogous to the Arnol\u0027d tongues which\nhave been extensively studied for a variety of dynamical systems, mostly\ndissipative ones. A rich variety of bifurcations of various types are observed,\nas well as period doubling cascades. Stability of periodic orbits is analyzed\nin detail.",
"arxiv_id": "quant-ph/0604006",
"authors": [
"Rebecca Hihinashvili",
"Tali Oliker",
"Yaniv S. Avizrats",
"Alexander Iomin",
"Shmuel Fishman",
"Italo Guarneri"
],
"categories": [
"quant-ph"
],
"doi": "10.1016/j.physd.2006.10.008",
"title": "Regimes of stability of accelerator modes",
"url": "https://arxiv.org/abs/quant-ph/0604006"
},
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