dorsal/arxiv
View SchemaSemi-classical Scar functions in phase space
| Authors | Alejandro M. F. Rivas |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0612220 |
| URL | https://arxiv.org/abs/quant-ph/0612220 |
| DOI | 10.1088/1751-8113/40/36/006 |
Abstract
We develop a semi-classical approximation for the scar function in the Weyl-Wigner representation in the neighborhood of a classically unstable periodic orbit of chaotic two dimensional systems. The prediction of hyperbolic fringes, asymptotic to the stable and unstable manifolds, is verified computationally for a (linear) cat map, after the theory is adapted to a discrete phase space appropriate to a quantized torus. Characteristic fringe patterns can be distinguished even for quasi-energies where the fixed point is not Bohr-quantized. Also the patterns are highly localized in the neighborhood of the periodic orbit and along its stable and unstable manifolds without any long distance patterns that appears for the case of the spectral Wigner function.
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"date_created": "2026-03-02T18:02:34.599000Z",
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"abstract": "We develop a semi-classical approximation for the scar function in the\n Weyl-Wigner representation in the neighborhood of a classically unstable\nperiodic orbit of chaotic two dimensional systems. The prediction of hyperbolic\nfringes, asymptotic to the stable and unstable manifolds, is verified\ncomputationally for a (linear) cat map, after the theory is adapted to a\ndiscrete phase space appropriate to a quantized torus. Characteristic fringe\npatterns can be distinguished even for quasi-energies where the fixed point is\nnot Bohr-quantized. Also the patterns are highly localized in the neighborhood\nof the periodic orbit and along its stable and unstable manifolds without any\nlong distance patterns that appears for the case of the spectral Wigner\nfunction.",
"arxiv_id": "quant-ph/0612220",
"authors": [
"Alejandro M. F. Rivas"
],
"categories": [
"quant-ph"
],
"doi": "10.1088/1751-8113/40/36/006",
"title": "Semi-classical Scar functions in phase space",
"url": "https://arxiv.org/abs/quant-ph/0612220"
},
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