Anomalous diffusion induced by enhancement of memory

Area of Science:

• Physics
• Statistical Mechanics
• Complex Systems

Background:

• Anomalous diffusion describes particle movement deviating from standard Brownian motion.
• Understanding the underlying mechanisms of anomalous diffusion is crucial in various scientific fields.

Purpose of the Study:

• To introduce simple microscopic non-Markovian walk models for anomalous diffusion.
• To investigate the role of memory effects in driving anomalous diffusion dynamics.

Main Methods:

• Development of non-Markovian walk models incorporating probability parameters.
• Analysis of two memory effect aspects: perfect memory and time-enhanced latest memory.
• Mathematical derivation of Hurst exponent relations for different memory models.

Main Results:

• Perfect memory model induces superdiffusion (Hurst exponent H = p for p>1/2).
• Latest memory enhancement models exhibit both superdiffusion and subdiffusion (H = (1+α)/2 and H = (1-α)/2 for 0 ≤ α ≤ 1).
• Time-enhanced latest memory leads to long-range correlations that increase over time.

Conclusions:

• Memory enhancement is a significant factor in anomalous diffusion.
• The proposed models provide a framework for understanding diffusion with memory effects.
• These findings offer insights into complex transport phenomena in various systems.