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arXiv:quant-ph/9810005 · International Journal of Bifurcation and Chaos

INTERNAL TIME PECULIARITIES AS A CAUSE OF BIFURCATIONS ARISING IN CLASSICAL TRAJECTORY PROBLEM AND QUANTUM CHAOS CREATION IN THREE-BODY SYSTEM

А. В. Богданов, Ashot S. Gevorkyan, A. G. Grigoryan, Stanislav A. Matveev

Published Nov 1, 1999• 7 citations
arXivHTMLPDF

Abstract

A new formulation of the theory of quantum mechanical multichannel scattering for three body collinear systems is proposed. It is shown that for this simple case, the principle of quantum determinism in the general case breaks down, and we have a micro-irreversible quantum mechanics. The first principle calculations of the quantum chaos (wave chaos) were pursued on the example of an elementary chemical reaction Li+(FH)→(LiFH)*→(LiF)+ H.

DOI
10.1142/s0218127499001590

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A new formulation of the theory of quantum mechanical multichannel scattering for three body collinear systems is proposed. It is shown that for this simple case, the principle of quantum determinism in the general case breaks down, and we have a micro-irreversible quantum mechanics. The first principle calculations of the quantum chaos (wave chaos) were pursued on the example of an elementary chemical reaction Li+(FH)→(LiFH)*→(LiF)+ H.
A new micro-irreversible 3D theory of quantum multichannel scattering in the three-body system is developed. The quantum approach is constructed on the generating trajectory tubes which allow taking into account influence of classical non-integrability on the dynamical quantum system. It was shown that when the volume of classical chaos in phase space is larger than quantum sell in the main object of quantum system the wavefunction generates chaos (quantum chaos). The probability of quantum transitions is constructed for this case. On the example of collinear collision of Li+(FH) -> (LiF)+H system is carried out the numerical calculation and was shown that in the system is generated quantum (wave) chaos.
By now the “chaos revolution” has reached nearly every branch of the natural sciences. In fact, chaos is everywhere. To name but a few examples, we talk about chaotic weather patterns, chaotic chemical reactions and the chaotic evolution of insect populations. Atomic and molecular physics are no exceptions. At first glance this is surprising since atoms and molecules are well described by the linear laws of quantum mechanics, while an essential ingredient of chaos is nonlinearity in the dynamic equations. Thus, chaos and atomic physics seem to have little to do with each other. But recently, atomic and molecular physicists have pushed the limits of their experiments to such high quantum numbers that it starts to make sense, in the spirit of Bohr's correspondence principle, to compare the results of atomic physics experiments with the predictions of classical mechanics, which, for the most part, show complexity and chaos. The most striking observation in recent years has been that quantum systems seem to “know” whether their classical counterparts display regular or chaotic motion. This fact can be understood intuitively on the basis of Feynman's version of quantum mechanics. In 1948 Feynman showed that quantum mechanics can be formulated on the basis of classical mechanics with the help of path integrals. Therefore it is expected that the quantum mechanics of an atom or molecule is profoundly influenced, but of course not completely determined, by the qualitative behaviour of its underlying classical mechanics.