ХАОТИЧНА ДИНАМІКА ДВОАТОМНИХ МОЛЕКУЛВ ЕЛЕКТРОМАГНІТНОМУ ПОЛІ

Автор(и)

  • A A Mashkantsev Одеський державний екологічний університет, Україна
  • A. V. Ignatenko Одеський державний екологічний університет, Україна
  • S V Kirianov Одеський державний екологічний університет, Україна
  • E V Pavlov Одеський державний екологічний університет,

DOI:

https://doi.org/10.18524/0235-2435.2018.27.150587

Ключові слова:

Nonlinear chaotic dynamics, diatomic molecules, electromagnetic field

Анотація

Моделюється нелінійна хаотична динаміка двоатомних молекул, взаємодіючих з резонансним лінійно-поляризованим електромагнітним полем. Представлена ефективна квантово-механічна модель для двоатомних молекули в електромагнітному полі, що базується на використанні рівняння Шредінгера і методу модельного потенціалу. Для детектування елементів хаотичної динаміки використані методи теорії хаосу і нелінійного аналізу, такі як алгоритм кореляційного інтеграла, аналіз на основі показників Ляпунова і ентропії Колмогорова, траєкторна модель прогнозу і ін. Представлені дані обчислення динамічних і топологічних інваріантів таких як кореляційна розмірність, розмірності вкладення і Каплана -Йорка, показники Ляпунова, ентропія Колмогорова і т. д. для часової залежності поляризації молекули ZrO, яка взаємодіє з лінійно-полярізованим електромагнітним полем. Отримані результати знаходяться в фізично розумній згоді з якісними висновками Бермана, Коловського, Заславського, Згана, Глушкова та ін.

Посилання

Lichtenberg, A. J. ; Lieberman, M. A. Regular and Stochastic Motion; Springer-Verlag: City, 1983.

Martin C.; Gutzwiller, G. Chaos in Classical and Quantum Mechanics; Springer-Verlag: New York, 1990.

Chirikov, B.V. A universal instability of many-dimensional oscillator systems. Phys. Rep. 1979, 52(5), 263-379.

Aurich, R.; Steiner, F. Statistical properties of highly excited quantum eigenstates of a strongly chaotic system. Physica D. 1993, 64, 185

Benvenuto, F.; Casati, G.; Shepelyansky, D.L. Rydberg Stabilization of atoms in strong fields: “magic” mountain in chaotic sea. Z.Phys.B. 1994, 94, 481-486.

Glushkov, A.V. Spectroscopy of atom and nucleus in a strong laser field: Stark effect and multiphoton resonances. J. Phys.: Conf. Ser. 2014, 548, 012020.

Berman, G.P.; Bulgakov, E.N.; Holm, D.D. Nonlinear resonance and dynamical chaos in a diatomic molecule driven by a resonant IR field. Phys. Rev. A 1995, 52, 3074-3080.

Zhang, C.; Katsouleas, T.; Joshi, C. Harmonic frequency generation and chaos in laser driven molecular vibrations. In Proc. of Shortwavelength Physics with Intense Laser Pulses, San-Diego, CA, March 29-31, 1993; Bederson, B., Walther, H., Eds.; Acad. Press: San Diego, 1993, pp 21-28.

López, G. V.; Mercado, A. P. Classical Chaos on Double Nonlinear Resonances in Diatomic Molecules. J. Mod. Phys. 2015, 6, 496-509.

Arango, C.A.; Kennerly, W.W.; Ezra, G.S. Classical and quantum mechanics of diatomic molecules in tilted fields. J. Chem. Phys.2005 , 122, 184303.

Ignatenko, A.V.; Buyadzhi ,A.; Buyadzhi, V.; Kuznetsova,A.; Mashkantsev,A.; Ternovsky, E. Nonlinear chaotic dynamics of quantum systems: molecules in an electromagnetic field// Adv. Quant. Chem. 2018,78 https://doi.org/10.1016/bs.aiq.2018.06.006.

Glushkov, A.V. True effective molecular valency Hamiltonian in a logical semiempricial theory. Journal of Structural Chem. 1988, 29(4), 495-501.

Glushkov, A.V. Operator Perturbation Theory for Atomic Systems in a Strong DC Electric Field. In Advances in Quantum Methods and Applications in Chemistry, Physics, and Biology, Series: Progress in Theoretical Chemistry and Physics; Hotokka, M., Brändas, E., Maruani, J., Delgado-Barrio, G., Eds.; Springer: Cham, 2013; Vol. 27, pp 161–177.

Malinovskaya, S.V.; Glushkov, A.V.; Khetselius, O.Yu.; Svinarenko, A.A.; Mischenko, E.V.; Florko, T.A. Optimized perturbation theory scheme for calculating the interatomic potentials and hyperfine lines shift for heavy atoms in the buffer inert gas. Int. J. Quant. Chem. 2009, 109(4), 3325-3329.

Glushkov, A.V.; Khetselius, O.Yu.; Malinovskaya, S.V. Optics and spectroscopy of cooperative laser-electron nuclear processes in atomic and molecular systems – new trend in quantum optics. Europ. Phys. Journ. ST 2008, 160, 195-204.

Glushkov, A.V.; Khetselius, O.Yu.; Malinovskaya, S.V. Spectroscopy of cooperative laser–electron nuclear effects in multiatomic molecules. Molec. Phys. 2008, 106, 1257-1260.

Glushkov, A.V.; Khetselius, O.Yu.; Svinarenko, A.A.; Serbov, N.G. The sea and ocean 3D acoustic waveguide: rays dynamics and chaos phenomena, J. Acoust. Soc. Amer. 2008, 123(5), 3625.

Bunyakova, Yu.Ya.; Glushkov, A.V.; Fedchuk, A.P.; Serbov, N.G.; Svinarenko, A.A.; Tsenenko, I.A. Sensing non-linear chaotic features in dynamics of system of coupled autogenerators: multifractal analysis, Sensor Electr. and Microsyst. Techn. 2007, Issue 1, 14-17.

Gottwald, G.A. ; Melbourne, I. Testing for chaos in deterministic systems with noise. Physica D. 2005, 212, 100-110.

Abarbanel, H.; Brown, R.; Sidorowich, J; Tsimring, L. The analysis of observed chaotic data in physical systems. Rev. Mod. Phys. 1993, 65, 1331- 1392.

Packard, N.; Crutchfield, J; Farmer, J.; Shaw, R. Geometry from a time series Phys. Rev. Lett. 1988, 45, 712-716.

Kennel, M.; Brown, R.; Abarbanel, H. Determining embedding dimension for phase-space reconstruction using a geometrical construction. Phys. Rev. A. 1992, 45, 3403-3412.

Gallager, R. Information theory and reliable communication. Wiley: N.-Y., 1986.

Grassberger, P. ; Procaccia, I. Measuring the strangeness of strange attractors. Physica D. 1983, 9, 189-208.

Theiler, J.; Eubank, S.; Longtin, A.; Galdrikian, B.; Farmer, J. Testing for nonlinearity in time series: The method of surrogate data. Physica D. 1992, 58, 77-94.

Sano, M.; Y. Sawada, Y. Measurement of the Lyapunov spectrum from chaotic time series. Phys Rev.Lett. 1995, 55, 1082-1085.

Glushkov, A.V. Methods of a Chaos Theory. OSENU: Odessa, 2012.

Glushkov, A.V.; Khetselius, O.Yu.; Brusentseva, S.V.; Zaichko, P.A.; Ternovsky, V.B. Studying interaction dynamics of chaotic systems within a non-linear prediction method: Application to neurophysiology In Advances in Neural Networks, Fuzzy Systems and Artificial Intelligence, Series: Recent Advances in Computer Engineering; Balicki, J., Ed.; WSEAS Press: Gdansk, 2014; Vol 21, pp 69-75.

Glushkov, A.V.; Prepelitsa, G.P.; Svinarenko, A.A. ; Zaichko, P.A. Studying interaction dynamics of the non-linear vibrational systems within non-linear prediction method (application to quantum autogenerators) In Dynamical Systems Theory; Awrejcewicz, J., Kazmierczak, M., Olejnik, P., Mrozowski, J., Eds.; Wyd. Politech. Łódz.: Łódz, 2013; Vol T1, pp 467-477.

Khetselius, O.Yu. Forecasting evolutionary dynamics of chaotic systems using advanced non-linear prediction method In Dynamical Systems Applications; Awrejcewicz, J., Kazmierczak, M., Olejnik, P., Mrozowski, J., Eds.; Wyd. Politech. Łódz.: Łódz, 2013; Vol T2, pp 145-152.

Khetselius, O.Yu.; Brusentseva, S.; Tkach, T.B. Studying interaction dynamics of chaotic systems within non-linear prediction method: Application to neurophysiology In Dynamical Systems Applications; Awrejcewicz, J., Kazmierczak, M., Olejnik, P., Mrozowski, J., Eds.; Wyd. Politech. Łódz.: Łódz, 2013; Vol T2, pp 251-259.

Glushkov, A.V.; Khetselius, O.Yu.; Brusentseva, S.; Duborez, A. Modeling chaotic dynamics of complex systems with using chaos theory, geometric attractors, and quantum neural networks. Proc. Intern. Geometry Center. 2014, 7(3), 87-94.

Glushkov, A.V.; Bunyakova, Yu.Ya.; Zaichko, P.A. Geometry of Chaos: Consistent combined approach to treating chaotic dynamics atmospheric pollutants and its forecasting. Proc. Intern. Geometry Center. 2013, 6(3),6-14.

Glushkov, A.V.; Lovett, L.; Khetselius, O.Yu.; Gurnitskaya, E.P.; Dubrovskaya, Yu.V.; Loboda, A.V. Generalized multiconfiguration model of decay of multipole giant resonances applied to analysis of reaction (μ - n) on the nucleus 40Ca. Int. J. Modern Phys. A. 2009, 24(2-3), 611-615

Khetselius, O.Yu.; Florko, T.A.; Svinarenko, A.A.; Tkach, T.B. Radiative and collisional spectroscopy of hyperfine lines of the Li-like heavy ions and Tl atom in an atmosphere of inert gas. Phys. Scripta. 2013, T153, 014037

Glushkov, A.V.; Malinovskaya, S.V.; Sukharev, D.E.; Khetselius, O.Yu.; Loboda, A.V.; Lovett, L. Green's function method in quantum chemistry: New numerical algorithm for the Dirac equation with complex energy and Fermi‐model nuclear potential. Int. Journ.Quant.Chem. 2009, 109, 1717-1727.

Khetselius, O.Yu. Relativistic calculating the hyperfine structure parameters for heavy-elements and laser detecting the isotopes and nuclear reaction products. Phys. Scripta. 2009, T135, 014023.

Svinarenko, A.A. Study of spectra for lanthanides atoms with relativistic many- body perturbation theory: Rydberg resonances. J. Phys.: Conf. Ser. 2014, 548, 012039

Glushkov, A.V.; Malinovskaya, S.V.; Gurnitskaya, E.P.; Khetselius, O.Yu.; Dubrovskaya, Yu.V. Consistent quantum theory of recoil induced excitation and ionization in atoms during capture of neutron. J. Phys.: Conf. Ser. 2006, 35, 425-430.

Glushkov, A.V.; Ambrosov, S.V.; Loboda, A.V.; Gurnitskaya, E.P.; Prepelitsa, G.P. Consistent QED approach to calculation of electron-collision excitation cross sections and strengths: Ne-like ions. Int. J. Quantum Chem. 2005, 104, 562-569.

Khetselius, O.Yu. Atomic parity non-conservation effect in heavy atoms and observing P and PT violation using NMR shift in a laser beam: To precise theory. J. Phys.: Conf. Ser. 2009, 194, 022009.

Glushkov, A.V.; Loboda, A.V.; Gurnitskaya, E.P.; Svinarenko, A.A. QED theory of radiation emission and absorption lines for atoms in a strong laser field. Phys. Scripta. 2009, 135, 014022.

Glushkov A.V.; Ivanov, L.N. DC strong-field Stark effect: consistent quantum-mechanical approach. J. Phys. B: At. Mol. Opt. Phys. 1993, 26, L379-386.

Khestelius, O.Yu. Hyperfine structure of atomic spectra. Astroprint: Odessa, 2008.

Glushkov, A.V. Relativistic multiconfiguration time-dependent self-consistent-field theory for molecules. Sov. Phys. Journal. 1991, 34(10), 871-876.

Glushkov, A.V.; Khetselius, O.Yu.; Svinarenko, A.A. Theoretical spectroscopy of autoionization resonances in spectra of lanthanide atoms. Phys. Scripta. 2013, T153, 014029.

Glushkov, A.V. Spectroscopy of cooperative muon-gamma-nuclear processes: Energy and spectral parameters J. Phys.: Conf. Ser. 2012, 397, 012011

Khetselius, O.Yu. Spectroscopy of cooperative electron-gamma-nuclear processes in heavy atoms: NEET effect. J. Phys.: Conf. Ser. 2012, 397, 012012.

Glushkov, A.V.; Khetselius, O.Yu.; Loboda, A.V.; Svinarenko, A.A. QED approach to atoms in a laser field: Multi-photon resonances and above threshold ionization In Frontiers in Quantum Systems in Chemistry and Physics, Series: Progress in Theoretical Chemistry and Physics; Wilson, S., Grout, P., Maruani, J., Delgado-Barrio, G., Piecuch, P., Eds.; Springer: Dordrecht, 2008; Vol. 18, pp 543-560.

Malinovskaya, S.V.; Glushkov, A.V.; Khetselius, O.Y. New Laser-Electron Nuclear Effects in the Nuclear γ Transition Spectra in Atomic and Molecular Systems. In Frontiers in Quantum Systems in Chemistry and Physics, Series: Progress in Theoretical Chemistry and Physics; Wilson, S., Grout, P., Maruani, J., Delgado-Barrio, G., Piecuch, P., Eds.; Springer: Dordrecht, 2008; Vol. 18, pp 525-541.

Glushkov, A.V.; Malinovskaya, S.V.; Chernyakova Y.G.; Svinarenko, A.A. Cooperative laser-electron-nuclear processes: QED calculation of electron satellites spectra for multi-charged ion in laser field. Int. Journ. Quant. Chem. 2004, 99, 889-893

Glushkov, A.V. Negative ions of inert gases. JETP Lett. 1992, 55, 97-100.

Glushkov, A.V.; Ivanov, L.N.; Ivanova, E.P. Autoionization Phenomena in Atoms. Moscow University Press, Moscow, 1986, 58-160

Malinovskaya, S.V.; Glushkov, A.V.; Khetselius, O.Yu.; Lopatkin, Yu.M.; Loboda, A.V.; Nikola, L.V.; Svinarenko, A.A.; Perelygina, T.B. Generalized energy approach for calculating electron collision cross‐sections for multicharged ions in a plasma: Debye shielding model, Int. J. Quant.Chem. 2011, 111(2), 288-296.

Buyadzhi, V.V. Laser multiphoton spectroscopy of atom embedded in Debye plasmas: multiphoton resonances and transitions. Photoelectronics. 2015, 24, 128-133.

Glushkov, A.V.; Malinovskaya, S.V.; Loboda, A.V.; Shpinareva, I.M.; Gurnitskaya, E.P.; Korchevsky, D.A. Diagnostics of the collisionally pumped plasma and search of the optimal plasma parameters of x-ray lasing: calculation of electron-collision strengths and rate coefficients for Ne-like plasma. J. Phys.: Conf. Ser. 2005, 11, 188-198.

Glushkov, A.V.; Khetselius, O.Yu.; Svinarenko, A.A. Relativistic theory of cooperative muon- -nuclear processes: Negative muon capture and metastable nucleus discharge. In Advances in the Theory of Quantum Systems in Chemistry and Physics, Series: Progress in Theoretical Chemistry and Physics; Hoggan, P., Brändas, E., Maruani, J., Delgado-Barrio, G., Piecuch, P. Eds.; Springer: Dordrecht, 2012; Vol. 22, pp 51–68.

Glushkov, A.V.; Khetselius, O.Yu.; Lovett, L. Electron-β-Nuclear Spectroscopy of Atoms and Molecules and Chemical Bond Effect on the β-Decay Parameters. In Advances in the Theory of Atomic and Molecular Systems Dynamics, Spectroscopy, Clusters, and Nanostructures, Series: Progress in Theoretical Chemistry and Physics; Piecuch, P., Maruani, J., Delgado-Barrio, G., Wilson, S., Eds.; Springer: Dordrecht, 2009; Vol. 20, pp 125–152.

Khetselius, O.Yu. Relativistic Energy Approach to Cooperative Electron-γ-Nuclear Processes: NEET Effect In Quantum Systems in Chemistry and Physics, Series: Progress in Theoretical Chemistry and Physics; Nishikawa, K., Maruani, J., Brändas, E., Delgado-Barrio, G., Piecuch, P., Eds.; Springer: Dordrecht, 2012; Vol. 26, pp 217-229.

Glushkov, A.V. Advanced Relativistic Energy Approach to Radiative Decay Processes in Multielectron Atoms and Multicharged Ions. In Quantum Systems in Chemistry and Physics: Progress in Methods and Applications, Series: Progress in Theoretical Chemistry and Physics; Nishikawa, K., Maruani, J., Brändas, E., Delgado-Barrio, G., Piecuch, P., Eds.; Springer: Dordrecht, 2012; Vol. 26, pp 231–252.

Khetselius, O.Yu. Relativistic perturbation theory calculation of the hyperfine structure parameters for some heavy-element isotopes. Int. Journ.Quant.Chem. 2009, 109, 3330-3335.

Ignatenko, A.V. Probabilities of the radiative transitions between Stark sublevels in spectrum of atom in an DC electric field: New approach. Photoelectronics, 2007, 16, 71-74.

Gurskaya, M.Yu.; Ignatenko, A.V.; Kvasikova, A.S.; Buyadzhi A.A. Advanced data for hydrogen atom in crossed electric and magnetic fields. Photoelectronics. 2017, 26, 148-155.

Glushkov, A.V. Atom in an electromagnetic field. KNT: Kiev, 2005.

Glushkov, A.V. Relativistic Quantum theory. Quantum mechanics of atomic systems. Astroprint: Odessa, 2008.

Khetselius, O.Yu. Quantum structure of electroweak interaction in heavy finite Fermi-systems. Astroprint: Odessa, 2011.

Glushkov, A.V.; Buyadzhi, V.V.; Ponomarenko, E.L. Geometry of Chaos: Advanced approach to treating chaotic dynamics in some nature systems// Proc. Intern. Geom. Center. 2014 7(1),24-30.

Pettersson, A.; Koivisto, R.; Lindgren, P.; Lundevall, S; Royen, P.; Sassenberg, U.; Shi, W. Electric Dipole Moment of the B1Π State of ZrO. J. Mol. Spectr. 2000, 200, 65-71.

Glushkov, A.V.; Khetselius,O.Yu.; Svinarenko,A.A.; Buyadzhi, V.V. Spectroscopy of autoionization states of heavy atoms and multiply charged ions (Odessa: TEC) -2015.

Huber, K.P.; Herzberg, G. Molecular spectra and molecular structure. IV. Constants of Diatomic Molecules; Van Nostrand Reinhold Co.: New York, 1979.

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2018-12-12

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