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Drift-controlled anomalous diffusion: a solvable Gaussian model

Lillo1, Mantegna

  • 1Istituto Nazionale per la Fisica della Materia, Unita di Palermo, Italy.

Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
|October 14, 2000
PubMed
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This study introduces a new Langevin equation with time-dependent drift, revealing diverse diffusion behaviors like subdiffusion and superdiffusion. The model also shows power-law relaxation dynamics in a harmonic potential.

Area of Science:

  • Statistical Physics
  • Stochastic Processes
  • Non-equilibrium Dynamics

Background:

  • Langevin equations are fundamental for modeling random processes.
  • Understanding anomalous diffusion is crucial in various scientific fields.
  • Time-dependent drift terms can lead to complex system dynamics.

Purpose of the Study:

  • Introduce a novel Langevin equation with a time-dependent drift.
  • Investigate the diverse diffusion behaviors arising from this model.
  • Analyze the system's response to an external harmonic potential.

Main Methods:

  • Formulating a Langevin equation with a power-law dependent drift.
  • Analyzing the variance dynamics of the stochastic process.
  • Studying the system's behavior under an external harmonic potential.

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Main Results:

  • The model describes diffusive, subdiffusive, superdiffusive, and stretched exponentially diffusive processes.
  • Specific parameter choices yield distinct diffusion regimes.
  • Relaxation to the stationary state in a harmonic potential exhibits power-law behavior.

Conclusions:

  • The proposed Langevin model offers a unified framework for various diffusion types.
  • The time-dependent drift is key to generating anomalous diffusion.
  • The model provides insights into relaxation dynamics in non-equilibrium systems.