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Non-Linear Chaotic Dynamics of Quantum Systems: Molecules in an Electromagnetic Field and Laser Systems

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Quantum Systems in Physics, Chemistry, and Biology

Part of the book series: Progress in Theoretical Chemistry and Physics ((PTCP,volume 30))

Abstract

We present a general, uniform chaos-geometric formalism to analysis, modelling and forecasting a non-linear chaotic dynamics of quantum systems (such as diatomic molecules in an electromagnetic infrared field, laser and quantum generators system etc.). The approach is based on using quantum-mechanical and kinetical models for quantum and laser systems combined with the advanced techniques such as a multi-fractal method, mutual information approach, correlation integral and false nearest neighbour algorithms, the Lyapunov exponent’s (LE) analysis, and surrogate data method, prediction models etc. The results of the numerical studying a chaotic dynamics of diatomic molecules (on example of the GeO molecule in an infrared field) and some laser systems are listed. There are presented data on the topological and dynamical invariants, in particular, the correlation, embedding, Kaplan-Yorke dimensions, LE, Kolmogorov’s entropy etc.

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Acknowledgements

Authors are thankful to Prof. E. Brändas, J. Maruani, A. Tadjer, R. Pavlov for the invitation to present an invited report at the workshop QSCP-XX (Bulgaria, 2015). The help in editing the manuscript by Mr. Heike Rossel and Ms. Heena Naveen (Springer) is very much appreciated.

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Authors and Affiliations

  1. Odessa State Environmental University, L’vovskaya str. 15, Odessa-9, 65016, Ukraine

    A. V. Glushkov, V. V. Buyadzhi, A. S. Kvasikova, A. V. Ignatenko, A. A. Kuznetsova, G. P. Prepelitsa & V. B. Ternovsky

Authors
  1. A. V. Glushkov
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  2. V. V. Buyadzhi
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  3. A. S. Kvasikova
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  4. A. V. Ignatenko
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  5. A. A. Kuznetsova
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  6. G. P. Prepelitsa
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  7. V. B. Ternovsky
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Corresponding author

Correspondence to A. V. Glushkov .

Editor information

Editors and Affiliations

  1. Chemistry and Pharmacy, University of Sofia, Sofia, Bulgaria

    Alia Tadjer

  2. Inst for Nuclear Res & Nuclear Ener, Sofia, Bulgaria

    Rossen Pavlov

  3. Laboratoire de Chimie Physique, CNRS & UPMC Laboratoire de Chimie Physique, Paris, France

    Jean Maruani

  4. Department of Quantum Chemistry, Uppsala University, Uppsala, Sweden

    Erkki J. Brändas

  5. CSIC, Madrid, Spain

    Gerardo Delgado-Barrio

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Glushkov, A.V. et al. (2017). Non-Linear Chaotic Dynamics of Quantum Systems: Molecules in an Electromagnetic Field and Laser Systems. In: Tadjer, A., Pavlov, R., Maruani, J., Brändas, E., Delgado-Barrio, G. (eds) Quantum Systems in Physics, Chemistry, and Biology. Progress in Theoretical Chemistry and Physics, vol 30. Springer, Cham. https://doi.org/10.1007/978-3-319-50255-7_10

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