dorsal/arxiv
View SchemaSensitivity to Initial Conditions in Quantum Dynamics: an Analytical Semiclassical Expansion
| Authors | K. M. Fonseca-Romero, M. C. Nemes, J. G. Peixoto de Faria, A. F. R. de Toledo Piza |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0201072 |
| URL | https://arxiv.org/abs/quant-ph/0201072 |
| DOI | 10.1016/j.physleta.2004.04.070 |
| Journal | Physics Letters A 327, 129 (2004) |
Abstract
We construct a class of systems for which quantum dynamics can be expanded around a mean field approximation with essentially classical content. The modulus of the quantum overlap of mean field states naturally introduces a classical distance between classical phase points. Using this fact we analytically show that the time rate of change (trc) of two neighbouring classical trajectories is directly proportional to the trc of quantum correlations. Coherence loss and nonlocality effects appear as corrections to mean field dynamics and we show that they can be given in terms of classical trajectories and generalized actions. This result is a first step in the connection between quantum and classically chaotic dynamics in the same sense of semiclassical expansions for the density of states. We apply the results to the nonintegrable (classically chaotic) version of the N-atom Jaynes-Cummings model.
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"abstract": "We construct a class of systems for which quantum dynamics can be expanded\naround a mean field approximation with essentially classical content.\n The modulus of the quantum overlap of mean field states naturally introduces\na classical distance between classical phase points. Using this fact we\nanalytically show that the time rate of change (trc) of two neighbouring\nclassical trajectories is directly proportional to the trc of quantum\ncorrelations. Coherence loss and nonlocality effects appear as corrections to\nmean field dynamics and we show that they can be given in terms of classical\ntrajectories and generalized actions. This result is a first step in the\nconnection between quantum and classically chaotic dynamics in the same sense\nof semiclassical expansions for the density of states. We apply the results to\nthe nonintegrable (classically chaotic) version of the N-atom Jaynes-Cummings\nmodel.",
"arxiv_id": "quant-ph/0201072",
"authors": [
"K. M. Fonseca-Romero",
"M. C. Nemes",
"J. G. Peixoto de Faria",
"A. F. R. de Toledo Piza"
],
"categories": [
"quant-ph"
],
"doi": "10.1016/j.physleta.2004.04.070",
"journal_ref": "Physics Letters A 327, 129 (2004)",
"title": "Sensitivity to Initial Conditions in Quantum Dynamics: an Analytical Semiclassical Expansion",
"url": "https://arxiv.org/abs/quant-ph/0201072"
},
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