Normal and anomalous diffusion in the disordered wind-tree model.

Area of Science:

• Statistical Mechanics
• Computational Physics
• Transport Phenomena

Background:

• The Ehrenfests' wind-tree model (EWTM) describes tracer particle dynamics in a system with scatterers.
• Understanding transport properties in disordered systems is crucial for various physical phenomena.

Purpose of the Study:

• To investigate the diffusive and subdiffusive transport of tracer particles in the EWTM using extensive simulations.
• To compare simulation results with theoretical predictions, particularly concerning the diffusion coefficient and non-Gaussian parameter.
• To model the van Hove correlation function for subdiffusive transport in overlapping scatterer systems.

Main Methods:

• Extensive event-driven molecular dynamics simulations were performed on the EWTM.
• Simulations were conducted at various reduced scatterer densities (ρ).
• Diffusion coefficients and non-Gaussian parameters were analyzed and compared with kinetic theory.

Main Results:

• For nonoverlapping scatterers, asymptotic motion is diffusive, with good agreement between simulation and theory at low densities.
• Deviations from kinetic theory emerge at higher densities, indicated by a maximum in the non-Gaussian parameter.
• For overlapping scatterers, asymptotic motion is subdiffusive (mean-squared displacement ~ t^{1-2ρ/3}), consistent with theoretical predictions.

Conclusions:

• Kinetic theory accurately predicts diffusion at low densities but deviates in the higher-density regime for the EWTM.
• The non-Gaussian parameter's behavior highlights deviations from simple diffusion.
• A proposed van Hove correlation function model quantitatively describes subdiffusive transport in systems with overlapping scatterers.