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Diffusive anomalies in a long-range Hamiltonian system.

Luis G Moyano1, Celia Anteneodo

  • 1Centro Brasileiro de Pesquisas Físicas-Rua Xavier Sigaud 150, 22290-180, Rio de Janeiro, Brazil.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|October 10, 2006
PubMed
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Anomalous diffusion in classical rotors (HMF model) shows superdiffusion in quasi-stationary states. Numerical analysis reveals q-Gaussian distributions, with diffusion depending on system size.

Area of Science:

  • Statistical mechanics
  • Non-equilibrium systems
  • Complex systems

Background:

  • The Hamiltonian Mean Field (HMF) model exhibits complex dynamics, including long-lived quasi-stationary states.
  • Superdiffusion of rotor phases has been previously reported in these states, indicating anomalous transport.

Purpose of the Study:

  • To investigate the anomalous diffusion in the HMF model by analyzing the full phase distributions.
  • To characterize the statistical properties of rotor phase evolution in quasi-stationary states.

Main Methods:

  • Numerical simulations of the HMF model.
  • Monitoring the evolution of unfolded phase distributions.
  • Fitting numerical histograms with q-Gaussian functions.
  • Analysis of the second moment of distributions.

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Main Results:

  • After a transient period, phase distributions fit the q-Gaussian form.
  • The parameter q increases with time, reaching a steady value near 3/2 (squared Lorentzian).
  • Diffusive motion in quasi-stationary states is strongly dependent on system size.

Conclusions:

  • The HMF model displays anomalous diffusion characterized by q-Gaussian distributions in quasi-stationary states.
  • The observed diffusion is non-ergodic and system-size dependent.
  • This study provides insights into transport phenomena in long-range interacting systems.