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Proceedings Paper

Decoherence and the quantum-classical limit in phase space
Author(s): Luiz Davidovich; F. Toscano; R. L. de Matos Filho
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Paper Abstract

We discuss the emergence of the classical description from quantum mechanics for chaotic systems. We consider a specific model, which corresponds to an ion trapped in a harmonic potential and submitted to a sequence of laser pulses: the kicked harmonic oscillator, under conditions that lead to chaotic behavior for the classical system. We show that noise plays an essential role in the transition from quantum to classical behavior. This transition is described in terms of the separation between the classical phase space distribution and the Wigner function corresponding to the quantum system, obtained by integrating over the whole phase space the magnitude of the difference between the two distributions. It is shown that, in the semiclassical limit, this separation is governed by a single parameter, which depends on the diffusion coefficient, the Lamb-Dicke parameter, and the kick strength. The Lamb-Dicke parameter plays the role of a dimensioneless Planck constant. As this parameter goes to zero, we show that both distributions remain close together for all times.

Paper Details

Date Published: 23 May 2005
PDF: 12 pages
Proc. SPIE 5842, Fluctuations and Noise in Photonics and Quantum Optics III, (23 May 2005); doi: 10.1117/12.609100
Show Author Affiliations
Luiz Davidovich, Univ. Federal do Rio de Janeiro (Brazil)
F. Toscano, Univ. Federal do Rio de Janeiro (Brazil)
R. L. de Matos Filho, Univ. Federal do Rio de Janeiro (Brazil)

Published in SPIE Proceedings Vol. 5842:
Fluctuations and Noise in Photonics and Quantum Optics III
Philip R. Hemmer; Julio R. Gea-Banacloche; Peter Heszler; M. Suhail Zubairy, Editor(s)

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