Anomalous diffusion of a dipole interacting with its surroundings

Area of Science:

• Statistical Physics
• Physical Chemistry
• Dielectric Spectroscopy

Background:

• The dynamics of dipoles in complex environments are crucial for understanding material properties.
• Existing models often simplify interactions or neglect anomalous diffusion effects.
• Inertial effects and molecular interactions significantly influence dielectric response.

Purpose of the Study:

• To develop a theoretical model for dipole dynamics incorporating anomalous diffusion.
• To analyze the linear dielectric response and complex susceptibility.
• To investigate the impact of interactions and inertial effects on spectral features.

Main Methods:

• Formulation of a fractional Fokker-Planck equation from Langevin equations.
• Solution in the frequency domain using matrix continued fractions.
• Analysis of extensive parameter ranges including damping and inertia ratios.

Main Results:

• The complex susceptibility exhibits a low-frequency band dependent on anomalous diffusion.
• A distinct far-infrared (THz) band with a comb-like peak structure was identified.
• The model successfully captures anomalous diffusion in interacting systems.

Conclusions:

• The study extends the cage model to anomalous diffusion, including inertial effects.
• The derived spectral features offer insights into molecular dynamics in complex media.
• This approach provides a framework for studying polar molecule dynamics with anomalous diffusion.