Manifestation of the Arnol'd Diffusion in Quantum Systems
Quantum Physics
2009-11-07 v2 Statistical Mechanics
Chaotic Dynamics
Atomic Physics
Abstract
We study an analog of the classical Arnol'd diffusion in a quantum system of two coupled non-linear oscillators one of which is governed by an external periodic force with two frequencies. In the classical model this very weak diffusion happens in a narrow stochastic layer along the coupling resonance, and leads to an increase of total energy of the system. We show that the quantum dynamics of wave packets mimics, up to some extent, global properties of the classical Arnol'd diffusion. This specific diffusion represents a new type of quantum dynamics, and may be observed, for example, in 2D semiconductor structures (quantum billiards) perturbed by time-periodic external fields.
Cite
@article{arxiv.quant-ph/0109147,
title = {Manifestation of the Arnol'd Diffusion in Quantum Systems},
author = {V. Ya. Demikhovskii and F. M. Izrailev and A. I. Malyshev},
journal= {arXiv preprint arXiv:quant-ph/0109147},
year = {2009}
}
Comments
RevTex, 4 pages including 7 ps-figures, corrected format