Russian Physics Journal

, Volume 51, Issue 8, pp 799–807 | Cite as

Structures of induced chaos

Elementary Particle Physics and Field Theory

A three-level model of spatial and temporal dynamic chaos induced by transitions from a quantum description of continuous medium motion to the classical limit is suggested. The basic microscopic level is formed by bundles of the Feynman trajectories corresponding to motion of individual quantum particles in the medium. The mesoscopic level forms differential distributions generated by a macroscopic drift of the basic trajectories. The macroscopic level itself is described by the phenomenological balance equations brought to a level of phase fibering of the mesoscopic model. An example of finding quantum trajectories is considered, and a general method of constructing induced mesostructures is described.


Jacobi Equation Quantum Particle Classical Trajectory Quantum Potential Dynamic Chaos 
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  1. 1.
    I. Imry, Introduction to Mesoscopic Physics [Russian translation], Fizmatlit, Moscow (2002).Google Scholar
  2. 2.
    Kh. Yu. Shtokman, Quantum Chaos [in Russian], Fizmatlit, Moscow (2004).Google Scholar
  3. 3.
    A. M. Mukhamedov, Turbulence: The Concept of Gauge Structures [in Russian], Publishing House of Kazan' State Technical University, Kazan' (2007).Google Scholar
  4. 4.
    C. D. Yang and C. H. Wei, Chaos, Solitons and Fractals, 33, 118–134 (2007).CrossRefMathSciNetGoogle Scholar
  5. 5.
    C. D. Yang, Ann. Phys., 319, 444–470 (2005).MATHCrossRefADSGoogle Scholar
  6. 6.
    M. S. El Naschie, Int. J. Nonlinear Sci. Numer. Simul., 6(4), 335–342 (2005).Google Scholar
  7. 7.
    M. S. El Naschie, Int. J. Nonlinear Sci. Numer. Simul., 8(1), 1–5 (2007).Google Scholar
  8. 8.
    A. M. Mukhamedov, Chaos, Solitons and Fractals, 33, 717–724 (2007).CrossRefGoogle Scholar
  9. 9.
    A. M. Mukhamedov, Fizich. Mezomekh., 10, No. 2, 53–61 (2007).MathSciNetGoogle Scholar
  10. 10.
    P. Pechucas, Phys. Rev. Lett., 51, 943 (1983).CrossRefMathSciNetADSGoogle Scholar

Copyright information

© Springer Science+Business Media, Inc. 2008

Authors and Affiliations

  1. 1.A. N. Tupolev Kazan’ State Technical UniversityKazan’Russia

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