Anomalous diffusion of a two-state random process in a constant bias field

Area of Science:

• Physics
• Statistical Mechanics
• Complex Systems

Background:

• The generalized Lévy walk with jumps (GLWJ) model describes complex particle transport.
• Understanding diffusive behaviors in biased fields is crucial for various physical and biological systems.

Purpose of the Study:

• To investigate the diffusive behaviors of the two-state GLWJ model under a constant biased field.
• To analyze the influence of power-law motion time and jump densities on particle transport.
• To explore the crossover phenomena in mean-squared displacement (MSD) and directional deviations in probability density functions (PDF).

Main Methods:

• Analysis of diffusive behaviors using mean-squared displacement (MSD).
• Calculation of the probability density function (PDF) to understand particle distribution.
• Modeling the generalized Lévy walk with jumps (GLWJ) with power-law motion time and Gaussian jump densities.

Main Results:

• The MSD exhibits a crossover phenomenon driven by three distinct mechanisms.
• The PDF shows directional deviation, indicating biased transport.
• A biased field does not always alter the diffusion outcome, contrary to initial expectations.
• Stronger fluctuation intensity can dominate diffusion over large timescales, irrespective of the diffusion exponent.

Conclusions:

• The biased GLWJ model displays rich and counterintuitive diffusion phenomena.
• Theoretical insights are provided for particle transport in biological and physical systems.
• Fluctuation intensity plays a critical role in determining long-term diffusive behavior.