Time-dependent perpendicular fluctuations in the driven lattice Lorentz gas

TL;DR

This study provides an exact analysis of perpendicular displacement fluctuations of a tracer particle on a lattice under force, considering obstacles, revealing complex time-dependent behaviors and deviations from free diffusion.

Contribution

It offers the first exact first-order in obstacle density evaluation of perpendicular fluctuations for all times and force strengths in a driven lattice Lorentz gas.

Findings

Perpendicular fluctuations are exactly evaluated in first order of obstacle density.

The non-Skellam parameter exhibits power-law growth at intermediate times.

The analysis links fluctuation behavior to diffusion coefficient and local exponents.

Abstract

We present results for the fluctuations of the displacement of a tracer particle on a planar lattice pulled by a step force in the presence of impenetrable, immobile obstacles. The fluctuations perpendicular to the applied force are evaluated exactly in first order of the obstacle density for arbitrarily strong pulling and all times. The complex time-dependent behavior is analyzed in terms of the diffusion coefficient, local exponent, and the non-Skellam parameter, which quantifies deviations from the dynamics on the lattice in the absence of obstacles. The non-Skellam parameter along the force is analyzed in terms of an asymptotic model and reveals a power-law growth for intermediate times.