Fractional hyper-ballistic transport under external oscillating electric fields

Area of Science:

• Statistical Physics
• Condensed Matter Physics
• Physical Chemistry

Background:

• Brownian motion theory describes particle dynamics, but real systems exhibit memory effects influencing particle displacement.
• Anomalous diffusion, deviating from linear time dependence, is observed in many experimental systems.
• The generalized Langevin equation (GLE) with fractional memory kernels effectively models complex systems with memory.

Purpose of the Study:

• To analytically solve the GLE for a tagged particle in a charged liquid subjected to external AC electric fields.
• To investigate the mean square displacement (MSD) behavior under different field conditions and memory kernel types.
• To identify and characterize unusual particle transport phenomena, such as hyper-ballistic diffusion.

Main Methods:

• Solving the generalized Langevin equation (GLE) with a fractional memory kernel analytically.
• Analyzing the mean square displacement (MSD) in both underdamped and overdamped regimes.
• Investigating the influence of external AC electric fields on particle dynamics.

Main Results:

• The MSD was decomposed into field-dependent and field-independent components.
• Time windows exhibiting unusual particle behaviors, including hyper-ballistic diffusion, were identified.
• Analytical solutions were obtained for the entire time scale, generalizing memoryless Brownian motion.

Conclusions:

• The study provides a comprehensive analytical solution for a fractional memory GLE in AC electric fields.
• New insights into anomalous diffusion and particle transport in complex media are presented.
• The findings generalize Brownian motion theory to include memory effects and external field influences.