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Anomalous transport: a deterministic approach.

Roberto Artuso1, Giampaolo Cristadoro

  • 1Center for Nonlinear and Complex Systems and Dipartimento di Scienze Chimiche, Fisiche e Matematiche, Università dell'Insubria, Via Valleggio 11, 22100 Como, Italy. Robert.Artuso@uninsubria.it

Physical Review Letters
|July 15, 2003
PubMed
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A new cycle-expansion technique deterministically computes transport moments. This method reveals phase transitions in one-dimensional intermittent maps and infinite horizon Lorentz gas transport spectra.

Area of Science:

  • Statistical physics
  • Dynamical systems theory
  • Transport phenomena

Background:

  • Understanding asymptotic transport behavior is crucial in complex systems.
  • Previous methods often lacked deterministic approaches for arbitrary order moments.
  • Intermittent maps and Lorentz gases present unique challenges due to their dynamics.

Purpose of the Study:

  • To introduce a novel, fully deterministic cycle-expansion technique.
  • To enable computation of asymptotic behavior for arbitrary order transport moments.
  • To analyze transport properties in specific one-dimensional systems.

Main Methods:

  • Development of a cycle-expansion (fully deterministic) method.
  • Application of the technique to one-dimensional intermittent maps.

Related Experiment Videos

  • Application to Lorentz gas models with an infinite horizon.

    • Main Results:

    • The cycle-expansion technique successfully computes asymptotic transport moments.
    • Confirmed the presence of phase transitions in the transport spectrum.
    • Demonstrated the technique's applicability to diverse complex systems.

    Conclusions:

    • The cycle-expansion method provides a robust framework for analyzing transport phenomena.
    • Phase transitions are a common feature in the studied systems' transport behavior.
    • This deterministic approach advances the theoretical understanding of complex dynamical systems.