Scaling of chaos in strongly nonlinear lattices

Mulansky, Mario

doi:10.1063/1.4868259

Title: Scaling of chaos in strongly nonlinear lattices

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Abstract

Although it is now understood that chaos in complex classical systems is the foundation of thermodynamic behavior, the detailed relations between the microscopic properties of the chaotic dynamics and the macroscopic thermodynamic observations still remain mostly in the dark. In this work, we numerically analyze the probability of chaos in strongly nonlinear Hamiltonian systems and find different scaling properties depending on the nonlinear structure of the model. We argue that these different scaling laws of chaos have definite consequences for the macroscopic diffusive behavior, as chaos is the microscopic mechanism of diffusion. This is compared with previous results on chaotic diffusion [M. Mulansky and A. Pikovsky, New J. Phys. 15, 053015 (2013)], and a relation between microscopic chaos and macroscopic diffusion is established.

Authors:

Mulansky, Mario ^[1]

Department of Physics and Astronomy, Potsdam University, Karl-Liebknecht-Str. 24, D-14476 Potsdam-Golm (Germany)

Publication Date:: Sun Jun 15 00:00:00 EDT 2014

OSTI Identifier:: 22250852

Resource Type:: Journal Article

Journal Name:: Chaos (Woodbury, N. Y.)

Additional Journal Information:: Journal Volume: 24; Journal Issue: 2; Other Information: (c) 2014 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 1054-1500

Country of Publication:: United States

Language:: English

Subject:: 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; CHAOS THEORY; COMPARATIVE EVALUATIONS; DIFFUSION; HAMILTONIANS; NONLINEAR PROBLEMS; PROBABILITY; SCALING LAWS

Citation Formats


                    Mulansky, Mario, Max-Planck-Institut für Physik komplexer Systeme, Nöthnitzer Str. 38, D-01187 Dresden, and Institut für Theoretische Physik, TU Dresden, Zellescher Weg 17, D-01069 Dresden. Scaling of chaos in strongly nonlinear lattices.  United States: N. p., 2014. 
        Web.  doi:10.1063/1.4868259.

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                    Mulansky, Mario, Max-Planck-Institut für Physik komplexer Systeme, Nöthnitzer Str. 38, D-01187 Dresden, & Institut für Theoretische Physik, TU Dresden, Zellescher Weg 17, D-01069 Dresden. Scaling of chaos in strongly nonlinear lattices.  United States.  https://doi.org/10.1063/1.4868259

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                    Mulansky, Mario, Max-Planck-Institut für Physik komplexer Systeme, Nöthnitzer Str. 38, D-01187 Dresden, and Institut für Theoretische Physik, TU Dresden, Zellescher Weg 17, D-01069 Dresden. 2014.  
        "Scaling of chaos in strongly nonlinear lattices".  United States.  https://doi.org/10.1063/1.4868259.

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@article{osti_22250852,

  title        = {Scaling of chaos in strongly nonlinear lattices},

  author       = {Mulansky, Mario and Max-Planck-Institut für Physik komplexer Systeme, Nöthnitzer Str. 38, D-01187 Dresden and Institut für Theoretische Physik, TU Dresden, Zellescher Weg 17, D-01069 Dresden},

  abstractNote = {Although it is now understood that chaos in complex classical systems is the foundation of thermodynamic behavior, the detailed relations between the microscopic properties of the chaotic dynamics and the macroscopic thermodynamic observations still remain mostly in the dark. In this work, we numerically analyze the probability of chaos in strongly nonlinear Hamiltonian systems and find different scaling properties depending on the nonlinear structure of the model. We argue that these different scaling laws of chaos have definite consequences for the macroscopic diffusive behavior, as chaos is the microscopic mechanism of diffusion. This is compared with previous results on chaotic diffusion [M. Mulansky and A. Pikovsky, New J. Phys. 15, 053015 (2013)], and a relation between microscopic chaos and macroscopic diffusion is established.},

  doi          = {10.1063/1.4868259},

  url          = {https://www.osti.gov/biblio/22250852},
  journal      = {Chaos (Woodbury, N. Y.)},

  issn         = {1054-1500},

  number       = 2,

  volume       = 24,

  place        = {United States},

  year         = {Sun Jun 15 00:00:00 EDT 2014},

  month        = {Sun Jun 15 00:00:00 EDT 2014}

}

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