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Random walk with chaotically driven bias.

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We studied random walks with fluctuating bias. The ensemble average of time-averaged variance (ETVAR) characterizes diffusion in time-quenched systems, unlike ETMSD, and shows linear growth.

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Area of Science:

  • Physics
  • Statistical Mechanics
  • Complex Systems

Background:

  • Random walks are fundamental models in statistical physics.
  • Fluctuating probabilities (bias) introduce complexity to random walk dynamics.
  • Understanding diffusion in non-standard random walks is crucial for various applications.

Purpose of the Study:

  • To investigate diffusive properties of random walks with fluctuating bias.
  • To compare 'time-quenched' and 'time-annealed' frameworks for biased random walks.
  • To identify appropriate metrics for characterizing diffusion in these systems.

Main Methods:

  • Analysis of a 'time-quenched' framework with deterministic bias time series (periodic, quasi-periodic, chaotic).
  • Analysis of a 'time-annealed' framework with stochastically generated fluctuating bias.
  • Calculation and comparison of ensemble average of time-averaged variance (ETVAR) and ensemble average of time-averaged mean square displacement (ETMSD).

Main Results:

  • ETVAR accurately characterizes diffusion in the time-quenched framework, showing linear time dependence.
  • ETMSD fails to capture diffusion in the time-quenched framework, even with zero net bias.
  • The time-annealed framework exhibits both normal and superdiffusion, analogous to Lévy walks.

Conclusions:

  • ETVAR is a reliable metric for diffusion in time-quenched biased random walks.
  • The choice of framework (time-quenched vs. time-annealed) significantly impacts diffusion characteristics.
  • Findings have potential applications in information and communication technologies, including energy transfer and search algorithms.