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Sublinear diffusion in the generalized triangle map.

Kensuke Yoshida1, Giulio Casati2,3, Shingo Watanabe1

  • 1Department of Physics, Tokyo Metropolitan University, Tokyo 192-0397, Japan.

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|August 17, 2022
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Summary
This summary is machine-generated.

Investigating diffusion in a generalized triangle map (GTM), this study finds sublinear diffusion of momentum. The momentum distribution follows a time-fractional diffusion equation, revealing unique non-Markovian yet stationary dynamics.

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Area of Science:

  • Dynamical Systems
  • Statistical Physics
  • Nonlinear Dynamics

Background:

  • Area-preserving maps are fundamental in understanding Hamiltonian systems.
  • Sublinear diffusion is a key phenomenon in complex systems, deviating from standard Brownian motion.
  • Generalized Triangle Maps (GTM) offer a nonchaotic model for studying diffusion properties.

Purpose of the Study:

  • To numerically and analytically investigate the diffusion of orbits within a generalized triangle map (GTM).
  • To characterize the statistical properties of momentum diffusion under generic perturbation parameters.
  • To determine if the observed diffusion dynamics align with known stochastic processes.

Main Methods:

  • Numerical simulations to track orbit diffusion and calculate mean-squared displacement.
  • Analytical investigation of the momentum distribution.
  • Comparison of observed dynamics with established models of sublinear diffusion.

Main Results:

  • Empirical evidence shows sublinear increase in mean-squared displacement of momentum over time.
  • The momentum distribution in the GTM adheres to a time-fractional diffusion equation.
  • Diffusion properties exhibit coexistence of non-Markovian and stationary characteristics, diverging from known processes.

Conclusions:

  • The generalized triangle map (GTM) exhibits unique sublinear diffusion dynamics.
  • The observed diffusion is characterized by a time-fractional diffusion equation.
  • The GTM presents a novel system for studying complex diffusion phenomena due to its non-Markovian yet stationary nature.