Normal-to-anomalous diffusion transition in disordered correlated potentials: from the central limit theorem to...

Area of Science:

• Statistical Physics
• Condensed Matter Physics
• Polymer Physics

Background:

• Studying particle diffusion in complex potentials is crucial for understanding various physical phenomena.
• Long-range correlations in potentials can significantly alter diffusion dynamics.
• Previous models often simplified potential correlations, limiting applicability.

Purpose of the Study:

• To investigate the diffusion of overdamped particles on a tilted random potential with long-range correlations.
• To establish a relationship between diffusion properties and the potential's correlation function.
• To explore the transition from normal to anomalous diffusion mechanisms.

Main Methods:

• Modeling the random potential using symbolic dynamics of shift spaces.
• Deriving a general formula for the diffusion coefficient under normal diffusion conditions.
• Analyzing the breakdown of the central limit theorem to predict anomalous diffusion.
• Employing numerical simulations to validate analytical predictions.

Main Results:

• Diffusion properties are directly linked to the potential's correlation function.
• A general formula for the diffusion coefficient was obtained for normal diffusion.
• Conditions for the breakdown of the central limit theorem leading to anomalous diffusion were identified.
• Analytical expressions for diffusion exponents in both normal and anomalous regimes were derived.

Conclusions:

• The correlation function of the random potential is a key determinant of particle diffusion behavior.
• The study provides a theoretical framework for understanding diffusion transitions in disordered systems.
• Numerical simulations confirm the analytical predictions, validating the proposed models.