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Distributional response to biases in deterministic superdiffusion.

Takuma Akimoto1

  • 1Department of Mechanical Engineering, Keio University, Yokohama, 223-8522, Japan. akimoto@z8.keio.jp

Physical Review Letters
|June 12, 2012
PubMed
Summary
This summary is machine-generated.

We discovered a new bias response in deterministic superdiffusion. The time-averaged velocity (TAV) is random, but its ensemble average shows a linear response to bias.

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Area of Science:

  • Physics
  • Statistical Mechanics
  • Dynamical Systems

Background:

  • Deterministic superdiffusion describes particle movement in complex systems.
  • Understanding responses to external biases is crucial for modeling transport phenomena.

Purpose of the Study:

  • To investigate the behavior of time-averaged velocity (TAV) in response to biases in deterministic superdiffusion.
  • To characterize the statistical properties of TAV and its distributional response.

Main Methods:

  • Utilizing infinite ergodic theory to analyze the reduced map of the system.
  • Applying a distributional limit theorem to understand the TAV response.

Main Results:

  • The time-averaged velocity (TAV) in the reduced map is intrinsically random.
  • The distribution of TAV follows the generalized arcsine distribution.
  • A bias induces a 'distributional response' observable in the TAV distribution.
  • The ensemble-averaged TAV response to bias is linear, despite individual randomness.

Conclusions:

  • Deterministic superdiffusion exhibits a novel distributional response to biases.
  • Infinite ergodic theory provides a framework for understanding these complex dynamics.
  • The linearity of the ensemble-averaged TAV contrasts with the intrinsic randomness of single trajectories.