Strong anomalous diffusive behaviors of the two-state random walk process

Area of Science:

• Physics
• Statistical Mechanics
• Complex Systems

Background:

• Two-state processes are prevalent in nature and require robust theoretical models.
• Existing models often simplify systems, neglecting the interplay between different motion states.

Purpose of the Study:

• To develop a theoretical framework, the two-state random walk (TSRW) model, for systems exhibiting alternating continuous-time random walk (CTRW) and Lévy walk (LW) behaviors.
• To analyze the anomalous diffusive properties arising from the combination of these two distinct states.

Main Methods:

• Analytical and numerical calculation of the mean squared displacement (MSD).
• Modeling the CTRW state with Gaussian jump length distribution and both states with power-law time distributions.
• Investigating the influence of different state mechanisms on diffusion characteristics.

Main Results:

• The TSRW model exhibits strong anomalous diffusion due to coexisting diffusion terms from both CTRW and LW states.
• The time distribution with the heavier tail dictates the overall diffusion behavior.
• Diffusion characteristics at long timescales depend on either the largest diffusion exponent or the largest diffusion coefficient, differing from single-state models.
• The model accurately describes particle motion in a velocity field, predicting subdiffusive behavior.

Conclusions:

• The TSRW model provides a more comprehensive understanding of anomalous diffusion in complex systems.
• The interplay between different random walk states leads to novel diffusion behaviors, including subdiffusion.
• This model has broad applicability in fields where particles transition between distinct modes of motion.