Persistent Sinai-type diffusion in Gaussian random potentials with decaying spatial correlations.

Area of Science:

• Physics
• Statistical Mechanics
• Condensed Matter Physics

Background:

• Logarithmic or Sinai-type subdiffusion is typically linked to random forces and nonstationary potentials.
• These potentials exhibit root-mean-squared amplitudes that increase with distance.

Purpose of the Study:

• To demonstrate the universal emergence of macroscopic logarithmic diffusion at low temperatures.
• To investigate its occurrence in stationary Gaussian random potentials with spatially decaying correlations.

Main Methods:

• Extensive computer simulations were conducted.
• A scaling approach was employed to analyze the diffusion behavior.
• A simple scaling theory was developed to explain the findings.

Main Results:

• Macroscopic logarithmic diffusion universally emerges at low temperatures in specific random potentials.
• Crossovers occur to power-law subdiffusion and then to normal diffusion with increasing temperature or time.
• The initial ultraslow diffusion is faster than the de Gennes-Bässler-Zwanzig limit.
• The ultraslow diffusion is nonergodic and shows local bias.

Conclusions:

• Stationary Gaussian random potentials with decaying correlations can lead to ultraslow logarithmic diffusion.
• The observed diffusion exhibits distinct crossover regimes.
• The developed scaling theory accurately explains numerical results and offers predictive capabilities.