dorsal/arxiv
View SchemaQuantum Arnol'd Diffusion in a Simple Nonlinear System
| Authors | V. Ya. Demikhovskii, F. M. Izrailev, A. I. Malyshev |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0205062 |
| URL | https://arxiv.org/abs/quant-ph/0205062 |
| DOI | 10.1103/PhysRevE.66.036211 |
| Journal | Phys.Rev. E66 (2002) 036211 |
Abstract
We study the fingerprint of the Arnol'd diffusion in a quantum system of two coupled nonlinear oscillators with a two-frequency external force. In the classical description, this peculiar diffusion is due to the onset of a weak chaos in a narrow stochastic layer near the separatrix of the coupling resonance. We have found that global dependence of the quantum diffusion coefficient on model parameters mimics, to some extent, the classical data. However, the quantum diffusion happens to be slower that the classical one. Another result is the dynamical localization that leads to a saturation of the diffusion after some characteristic time. We show that this effect has the same nature as for the studied earlier dynamical localization in the presence of global chaos. The quantum Arnol'd diffusion represents a new type of quantum dynamics and can be observed, for example, in 2D semiconductor structures (quantum billiards) perturbed by time-periodic external fields.
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"abstract": "We study the fingerprint of the Arnol\u0027d diffusion in a quantum system of two\ncoupled nonlinear oscillators with a two-frequency external force. In the\nclassical description, this peculiar diffusion is due to the onset of a weak\nchaos in a narrow stochastic layer near the separatrix of the coupling\nresonance. We have found that global dependence of the quantum diffusion\ncoefficient on model parameters mimics, to some extent, the classical data.\nHowever, the quantum diffusion happens to be slower that the classical one.\nAnother result is the dynamical localization that leads to a saturation of the\ndiffusion after some characteristic time. We show that this effect has the same\nnature as for the studied earlier dynamical localization in the presence of\nglobal chaos. The quantum Arnol\u0027d diffusion represents a new type of quantum\ndynamics and can be observed, for example, in 2D semiconductor structures\n(quantum billiards) perturbed by time-periodic external fields.",
"arxiv_id": "quant-ph/0205062",
"authors": [
"V. Ya. Demikhovskii",
"F. M. Izrailev",
"A. I. Malyshev"
],
"categories": [
"quant-ph",
"astro-ph",
"cond-mat.stat-mech",
"nlin.CD",
"physics.atom-ph"
],
"doi": "10.1103/PhysRevE.66.036211",
"journal_ref": "Phys.Rev. E66 (2002) 036211",
"title": "Quantum Arnol\u0027d Diffusion in a Simple Nonlinear System",
"url": "https://arxiv.org/abs/quant-ph/0205062"
},
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