Lévy Walk Dynamics in an External Constant Force Field in Non-Static Media

Area of Science:

• Statistical Physics
• Non-equilibrium Systems
• Complex Systems

Background:

• Transport properties of diffusion particles significantly change in non-static media.
• Lévy walk models are crucial for describing anomalous diffusion.
• Understanding particle behavior under external forces in dynamic environments is essential.

Purpose of the Study:

• To investigate a Lévy walk model subjected to an external constant force in non-static media.
• To derive and analyze the master equation governing particle probability density in comoving coordinates.
• To explore statistical properties and emergent phenomena in this complex system.

Main Methods:

• Transformation of the physical coordinate system to a comoving coordinate system using a scale factor.
• Derivation of the master equation for the probability density function.
• Application of Hermite orthogonal polynomial expansions to obtain statistical properties.

Main Results:

• Asymptotic behaviors of the first two moments and kurtosis were derived in both physical and comoving coordinates.
• Striking phenomena were observed due to the interplay of non-static media, external force, and stochastic motion.
• Stationary distributions were analyzed for specific cases via numerical simulations.

Conclusions:

• The study provides a theoretical framework for understanding diffusion in dynamic, forced environments.
• The interplay between media dynamics, external forces, and intrinsic stochasticity leads to complex behaviors.
• Results offer insights into non-equilibrium statistical mechanics and transport phenomena.