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Area of Science:

  • Physics
  • Statistical Mechanics
  • Complex Systems

Background:

  • Aging phenomena are prevalent in various physical systems.
  • Statistical quantities in aging anomalous diffusion depend on aging time (ta).

Purpose of the Study:

  • To investigate the effect of external force fields on aging Lévy walks.
  • To compare the influence of constant and time-dependent periodic forces.

Main Methods:

  • Utilizing the Langevin picture of Lévy walks.
  • Applying the generalized Green-Kubo formula.
  • Analyzing ensemble- and time-averaged mean-squared displacements in weak (ta≪t) and strong (ta≫t) aging regimes.

Main Results:

  • A constant force field is identified as crucial for inducing and enhancing aging phenomena in Lévy walks.
  • Time-dependent periodic forces do not exhibit the same enhancing effect on aging Lévy walks.
  • Theoretical analyses and numerical simulations confirm these distinct effects.

Conclusions:

  • External force fields significantly modulate aging Lévy walk dynamics.
  • Constant forces promote diffusion, while periodic forces do not, highlighting the importance of force characteristics.