Time-dependent perpendicular fluctuations in the driven lattice Lorentz gas.

Area of Science:

• Statistical Mechanics
• Condensed Matter Physics
• Computational Physics

Background:

• Studying tracer particle dynamics is crucial for understanding transport phenomena in complex media.
• Impenetrable obstacles significantly alter particle motion compared to free lattice diffusion.

Purpose of the Study:

• To investigate the fluctuations of a tracer particle's displacement on a lattice with obstacles under a step force.
• To quantify deviations from standard lattice dynamics caused by obstacles.

Main Methods:

• Exact evaluation of perpendicular fluctuations to the applied force in first order of obstacle density.
• Analysis of time-dependent behavior using diffusion coefficient, local exponent, and non-Skellam parameter.
• Asymptotic modeling of the non-Skellam parameter along the force direction.

Main Results:

• Exact results for perpendicular fluctuations are obtained for strong pulling and all times.
• The non-Skellam parameter quantifies deviations from obstacle-free lattice dynamics.
• A power-law growth of the non-Skellam parameter along the force is observed for intermediate times.

Conclusions:

• Impenetrable obstacles introduce complex, time-dependent behaviors in tracer particle displacement.
• The non-Skellam parameter is a key metric for characterizing these deviations.
• The observed power-law growth provides insights into the intermediate-time dynamics.