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Physics Reports

Relevance of classical chaos in quantum mechanics: The hydrogen atom in a monochromatic field

Giulio Casati

Published Oct 1, 1987• 357 citations
Publisher
DOI
10.1016/0370-1573(87)90009-3

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The quantum domain behaviour of a classical double-well oscillator which exhibits chaos in the presence of an external monochromatic field has been studied using Bohmian mechanics. The classical Kolmogorov-Arnol'd-Moser (KAM) tori break down in the presence of an external perturbation for which the corresponding quantal phase portrait exhibits regular islands owing to the quantum suppression of the classical chaos. It has also been observed that the classical chaos generally enhances the quantum fluctuations.

•May 25, 1999•4 citations
The statistics of quantum Poincare recurrences in Hilbert space for diamagnetic hydrogen atom in strong magnetic field has been investigated. It has been shown that quantities characterizing classical chaos are in a good agreement with the ones that are used to describe quantum chaos. The equality of classical and quantum Poincare recurrences has been shown. It has been proved that one of the signs of the emergence of quantum chaos is the irreversible transition from a pure quantum mechanical state to the mixed one.
The quantum localization phenomenon that strongly limits any quantum process of diffusive ionization that may be started in systems subjected to a periodic perturbation is discussed. In the case of a highly excited hydrogen atom in a monochromatic field, this phenomenon is theoretically analyzed by reducing the dynamics to appropriate mappings. It is shown that if the field strength is less than a so-called delocalization border, the distribution over unperturbed levels is exponential in the number of absorbed photons and the corresponding localization length is determined. Using the mapping description, it is shown that the excitation process occurring in a two-dimensional atom proceeds essentially along the same lines as in the one-dimensional model. These predictions are supported by results of numerical simulation, and the possibility of their experimental verification is discussed.>
The quantum domain behaviour of a classical double-well oscillator which exhibits chaos in the presence of an external monochromatic field has been studied using Bohmian mechanics. The classical Kolmogorov-Arnol'd-Moser (KAM) tori break down in the presence of an external perturbation for which the corresponding quantal phase portrait exhibits regular islands owing to the quantum suppression of the classical chaos. It has also been observed that the classical chaos generally enhances the quantum fluctuations.