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Ratchet current and scaling properties in a nontwist mapping

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Listed:
  • Rolim Sales, Matheus
  • Borin, Daniel
  • de Souza, Leonardo Costa
  • Szezech Jr., José Danilo
  • Viana, Ricardo Luiz
  • Caldas, Iberê Luiz
  • Leonel, Edson Denis

Abstract

We investigate the transport of particles in the chaotic component of phase space for a two-dimensional, area-preserving nontwist map. The survival probability for particles within the chaotic sea is described by an exponential decay for regions in phase space predominantly chaotic and it is scaling invariant in this case. Alternatively, when considering mixed chaotic and regular regions, there is a deviation from the exponential decay, characterized by a power law tail for long times, a signature of the stickiness effect. Furthermore, due to the asymmetry of the chaotic component of phase space with respect to the line I=0, there is an unbalanced stickiness that generates a ratchet current in phase space. Finally, we perform a phenomenological description of the diffusion of chaotic particles by identifying three scaling hypotheses, and obtaining the critical exponents via extensive numerical simulations.

Suggested Citation

  • Rolim Sales, Matheus & Borin, Daniel & de Souza, Leonardo Costa & Szezech Jr., José Danilo & Viana, Ricardo Luiz & Caldas, Iberê Luiz & Leonel, Edson Denis, 2024. "Ratchet current and scaling properties in a nontwist mapping," Chaos, Solitons & Fractals, Elsevier, vol. 189(P1).
    • Handle: RePEc:eee:chsofr:v:189:y:2024:i:p1:s0960077924011664
    DOI: 10.1016/j.chaos.2024.115614
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    References listed on IDEAS

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    1. Borin, Daniel, 2024. "Caputo fractional standard map: Scaling invariance analyses," Chaos, Solitons & Fractals, Elsevier, vol. 181(C).
    2. Leonel, Edson D. & Livorati, André L.P., 2008. "Describing Fermi acceleration with a scaling approach: The Bouncer model revisited," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(5), pages 1155-1160.
    3. Borin, Daniel & Livorati, André Luís Prando & Leonel, Edson Denis, 2023. "An investigation of the survival probability for chaotic diffusion in a family of discrete Hamiltonian mappings," Chaos, Solitons & Fractals, Elsevier, vol. 175(P1).
    4. Edson D. Leonel, 2009. "Phase Transition in Dynamical Systems: Defining Classes of Universality for Two-Dimensional Hamiltonian Mappings via Critical Exponents," Mathematical Problems in Engineering, Hindawi, vol. 2009, pages 1-22, October.
    5. Méndez-Bermúdez, J.A. & Peralta-Martinez, Kevin & Sigarreta, José M. & Leonel, Edson D., 2023. "Leaking from the phase space of the Riemann–Liouville fractional standard map," Chaos, Solitons & Fractals, Elsevier, vol. 172(C).
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