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Related Experiment Videos

Field-induced dispersion in subdiffusion.

I M Sokolov1, J Klafter

  • 1Institut für Physik, Humboldt Universität zu Berlin, Newtonstrasse 15, 12489 Berlin, Germany.

Physical Review Letters
|December 13, 2006
PubMed
Summary
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Continuous-time random walks under oscillating fields exhibit unique behaviors. For specific power-law waiting times, the particle

Area of Science:

  • Physics
  • Statistical Mechanics
  • Nonlinear Dynamics

Background:

  • Continuous-time random walks (CTRWs) are fundamental models in statistical physics.
  • Understanding CTRW response to external fields is crucial for various applications.
  • Non-Markovian dynamics and nonstationarity introduce complex behaviors.

Purpose of the Study:

  • To investigate the response of CTRWs to an oscillating external field.
  • To analyze the time dependence of the first two moments of particle displacement.
  • To explore the impact of nonstationary semi-Markovian dynamics on CTRW behavior.

Main Methods:

  • Utilizing the generalized master equation approach.
  • Focusing on power-law waiting-time distributions (0 < alpha < 1).

Related Experiment Videos

  • Analyzing the mean particle position and the dispersion of particle position.

    • Main Results:

    • For 0 < alpha < 1, the mean particle position converges to a constant, indicating response decay.
    • An additional time-dependent contribution to particle position dispersion arises.
    • This dispersion grows proportionally to the square of the oscillating field's amplitude.

    Conclusions:

    • Nonstationary CTRWs exhibit distinct responses to oscillating fields.
    • The decay of the mean response and the growth of dispersion are direct consequences of nonstationarity.
    • These phenomena are experimentally observable and offer insights into complex systems.