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Stability, isolated chaos, and superdiffusion in nonequilibrium many-body interacting systems.

Atanu Rajak1,2, Itzhack Dana1

  • 1Department of Physics, Bar-Ilan University, Ramat Gan 5290002, Israel.

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We discovered stable orbits in chaotic systems with interacting particles, featuring ballistic motion. These stable zones, or isolated chaotic zones (ICZ), exhibit slower diffusion, leading to superdiffusion in kinetic energy.

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Area of Science:

  • Statistical Mechanics
  • Non-equilibrium Physics
  • Dynamical Systems

Background:

  • Many-body systems with interactions and periodic driving exhibit complex dynamics.
  • Understanding stability and transport in non-integrable systems is crucial for statistical mechanics.

Purpose of the Study:

  • To investigate stability and chaotic transport in paradigmatic non-equilibrium many-body systems.
  • To rigorously prove the existence of stable orbits in strongly non-integrable regimes.

Main Methods:

  • Analytical methods to rigorously show the existence of stable orbits.
  • Numerical simulations to demonstrate the properties of isolated chaotic zones (ICZ).

Main Results:

  • Existence of fully stable orbits, accelerator-mode (AM) fixed points, with ballistic momentum motion.
  • Identification of isolated chaotic zones (ICZ) localized around AM fixed points.
  • Superdiffusion observed in the mean kinetic energy of initial ensembles containing an ICZ.

Conclusions:

  • Stable orbits can persist in strongly chaotic many-body systems.
  • Isolated chaotic zones exhibit significantly slower Arnold diffusion.
  • The findings challenge conventional understanding of chaotic transport in non-equilibrium systems.