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Dynamical Systems Theory and Applications

DSTA 2019: Perspectives in Dynamical Systems II: Mathematical and Numerical Approaches pp 113–123Cite as

Nonlinear Dynamics of Atomic and Molecular Systems in an Electromagnetic Field: Deterministic Chaos and Strange Attractors

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Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS,volume 363)

Abstract

We present a new mathematical approach to studying deterministic chaos and strange attractors in dynamics of nonlinear processes in atomic and molecular systems in an electromagnetic field. To treat chaotic dynamics of systems it is constructed effective scheme that includes new quantum-dynamic models (based on the finite-difference solution of the Schrödinger equation, optimized operator perturbation theory and realistic model potential for quantum systems) and advanced nonlinear analysis and a chaos theory methods such as power spectrum analysis, the correlation integral algorithm, the fractal method, the Lyapunov’s exponents and Kolmogorov entropy analysis, etc. Availability of multiple resonances with super little widths in spectrum of an atom in external magnetic field is treated and provided by interference phenomena and fluctuations. Dynamics of resonances in spectrum of diatomic molecule in the infrared electromagnetic field is considered and the topological and dynamical invariants are recalculated.

Keywords

  • Nonlinear dynamics
  • Atomic systems
  • Electromagnetic field
  • Chaos
  • Resonances

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Author information

Authors and Affiliations

  1. Odessa State Environmental University, Odessa, Ukraine

    Alexander V. Glushkov, Anna V. Ignatenko, Alexandra O. Makarova & Eugeny V. Ternovsky

  2. National University “Odessa Maritime Academy”, Odessa, Ukraine

    Anna A. Kuznetsova

  3. National University “Odessa Law Academy”, Odessa, Ukraine

    Elena V. Bakunina & Oleg V. Dykyi

Authors
  1. Alexander V. Glushkov
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  2. Anna V. Ignatenko
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  3. Anna A. Kuznetsova
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  4. Elena V. Bakunina
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  6. Alexandra O. Makarova
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  7. Eugeny V. Ternovsky
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Editors and Affiliations

  1. Department of Automation, Biomechanics and Mechatronics, Lodz University of Technology, Lodz, Poland

    Prof. Jan Awrejcewicz

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Glushkov, A.V. et al. (2021). Nonlinear Dynamics of Atomic and Molecular Systems in an Electromagnetic Field: Deterministic Chaos and Strange Attractors. In: Awrejcewicz, J. (eds) Perspectives in Dynamical Systems II: Mathematical and Numerical Approaches. DSTA 2019. Springer Proceedings in Mathematics & Statistics, vol 363. Springer, Cham. https://doi.org/10.1007/978-3-030-77310-6_11

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