Time-Dependent Fluctuations and Superdiffusivity in the Driven Lattice Lorentz Gas

TL;DR

This paper analyzes the transient and stationary fluctuation dynamics of a driven tracer particle in a lattice with obstacles, revealing superdiffusive behavior at intermediate times and a force-enhanced diffusion constant.

Contribution

It provides an exact analytical solution for the transient fluctuations of a driven tracer in a lattice with obstacles, valid at low obstacle density and strong driving.

Findings

Fluctuations grow superdiffusively at intermediate times under strong driving.

In the stationary state, fluctuations become diffusive regardless of initial superdiffusivity.

The diffusion constant increases nonlinearly with the applied force.

Abstract

We consider a tracer particle on a lattice in the presence of immobile obstacles. Starting from equilibrium, a force pulling on the particle is switched on, driving the system to a new stationary state. We solve for the complete transient dynamics of the fluctuations of the tracer position along the direction of the force. The analytic result, exact in first order of the obstacle density and for arbitrarily strong driving, is compared to stochastic simulations. Upon strong driving, the fluctuations grow superdiffusively for intermediate times; however, they always become diffusive in the stationary state. The diffusion constant is nonanalytic for small driving and is enhanced by orders of magnitude by increasing the force.