dorsal/arxiv
View SchemaSemiclassical structure of chaotic resonance eigenfunctions
| Authors | J. P. Keating, M. Novaes, S. D. Prado, M. Sieber |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0605217 |
| URL | https://arxiv.org/abs/quant-ph/0605217 |
| DOI | 10.1103/PhysRevLett.97.150406 |
| Journal | Phys. Rev. Lett. 97, 150406 (2006) |
Abstract
We study the resonance (or Gamow) eigenstates of open chaotic systems in the semiclassical limit, distinguishing between left and right eigenstates of the non-unitary quantum propagator, and also between short-lived and long-lived states. The long-lived left (right) eigenstates are shown to concentrate as $\hbar\to 0$ on the forward (backward) trapped set of the classical dynamics. The limit of a sequence of eigenstates $\{\psi(\hbar)\}_{\hbar\to 0}$ is found to exhibit a remarkably rich structure in phase space that depends on the corresponding limiting decay rate. These results are illustrated for the open baker map, for which the probability density in position space is observed to have self-similarity properties.
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"abstract": "We study the resonance (or Gamow) eigenstates of open chaotic systems in the\nsemiclassical limit, distinguishing between left and right eigenstates of the\nnon-unitary quantum propagator, and also between short-lived and long-lived\nstates. The long-lived left (right) eigenstates are shown to concentrate as\n$\\hbar\\to 0$ on the forward (backward) trapped set of the classical dynamics.\nThe limit of a sequence of eigenstates $\\{\\psi(\\hbar)\\}_{\\hbar\\to 0}$ is found\nto exhibit a remarkably rich structure in phase space that depends on the\ncorresponding limiting decay rate. These results are illustrated for the open\nbaker map, for which the probability density in position space is observed to\nhave self-similarity properties.",
"arxiv_id": "quant-ph/0605217",
"authors": [
"J. P. Keating",
"M. Novaes",
"S. D. Prado",
"M. Sieber"
],
"categories": [
"quant-ph",
"nlin.CD"
],
"doi": "10.1103/PhysRevLett.97.150406",
"journal_ref": "Phys. Rev. Lett. 97, 150406 (2006)",
"title": "Semiclassical structure of chaotic resonance eigenfunctions",
"url": "https://arxiv.org/abs/quant-ph/0605217"
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