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Proceedings Paper

The study of classical dynamical systems using quantum theory
Author(s): Yu. I. Bogdanov; N. A. Bogdanova
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Paper Abstract

We have developed a method for complementing an arbitrary classical dynamical system to a quantum system using the Lorenz and Rössler systems as examples. The Schrödinger equation for the corresponding quantum statistical ensemble is described in terms of the Hamilton-Jacobi formalism. We consider both the original dynamical system in the coordinate space and the conjugate dynamical system corresponding to the momentum space. Such simultaneous consideration of mutually complementary coordinate and momentum frameworks provides a deeper understanding of the nature of chaotic behavior in dynamical systems. We have shown that the new formalism provides a significant simplification of the Lyapunov exponents calculations. From the point of view of quantum optics, the Lorenz and Rössler systems correspond to three modes of a quantized electromagnetic field in a medium with cubic nonlinearity. From the computational point of view, the new formalism provides a basis for the analysis of complex dynamical systems using quantum computers.

Paper Details

Date Published: 18 December 2014
PDF: 9 pages
Proc. SPIE 9440, International Conference on Micro- and Nano-Electronics 2014, 94401J (18 December 2014); doi: 10.1117/12.2181076
Show Author Affiliations
Yu. I. Bogdanov, Institute of Physics and Technology (Russian Federation)
National Research Univ. of Electronic Technology (Russian Federation)
National Research Nuclear Univ. MEPHI (Russian Federation)
N. A. Bogdanova, National Research Univ. of Electronic Technology (Russian Federation)


Published in SPIE Proceedings Vol. 9440:
International Conference on Micro- and Nano-Electronics 2014
Alexander A. Orlikovsky, Editor(s)

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