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Adrián A Budini1

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We developed a discrete random-walk model with global memory effects. This model exhibits ballistic behavior and inhomogeneous diffusion, revealing memory

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Area of Science:

  • Statistical Mechanics
  • Complex Systems

Background:

  • Random-walk models are fundamental in physics.
  • Memory effects can significantly alter system dynamics.

Purpose of the Study:

  • Introduce a novel discrete random-walk model with global memory.
  • Analyze the impact of memory on diffusion and ergodic properties.

Main Methods:

  • Exact calculation of the characteristic function.
  • Analytical study of time-averaged moments for ergodic properties.
  • Investigation of probability densities for time and ensemble averages.

Main Results:

  • The model demonstrates ballistic ensemble behavior.
  • Individual trajectories exhibit inhomogeneous diffusion.
  • Time-averaged moments remain random objects, deviating from ensemble averages.

Conclusions:

  • Global memory effects induce non-Markovian and inhomogeneous diffusion.
  • Ergodic properties are significantly impacted by memory.
  • A generalized Einstein fluctuation-dissipation relation is derived.