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Chaotic solitons in driven sine-Gordon model

Author

Listed:
  • Levkov, D.G.
  • Maslov, V.E.
  • Nugaev, E.Ya.

Abstract

Profiles of static solitons in one-dimensional scalar field theory satisfy the same equations as trajectories of a fictitious particle in multidimensional mechanics. We argue that the structure and properties of the solitons are essentially different if the respective mechanical motions are chaotic. This happens in multifield models and models with spatially dependent potential. We illustrate our findings using one-field sine-Gordon model in external Dirac comb potential. First, we show that the number of different “chaotic” solitons grows exponentially with their length, and the growth rate is related to the topological entropy of the mechanical system. Second, the field values of stable solitons form a fractal; we compute its box-counting dimension. Third, we demonstrate that the distribution of field values in the fractal is related to the metric entropy of the analogous mechanical system.

Suggested Citation

  • Levkov, D.G. & Maslov, V.E. & Nugaev, E.Ya., 2020. "Chaotic solitons in driven sine-Gordon model," Chaos, Solitons & Fractals, Elsevier, vol. 139(C).
    • Handle: RePEc:eee:chsofr:v:139:y:2020:i:c:s0960077920304768
    DOI: 10.1016/j.chaos.2020.110079
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    References listed on IDEAS

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    1. Thomas Schweigler & Valentin Kasper & Sebastian Erne & Igor Mazets & Bernhard Rauer & Federica Cataldini & Tim Langen & Thomas Gasenzer & Jürgen Berges & Jörg Schmiedmayer, 2017. "Experimental characterization of a quantum many-body system via higher-order correlations," Nature, Nature, vol. 545(7654), pages 323-326, May.
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