Ehrenfest Wind-Tree Model is Dynamically Richer Than the Lorentz Gas

TL;DR

This paper shows that a physical version of the Wind-Tree model exhibits more complex superdiffusive behaviors than the Lorentz gas, including a novel regime with diffusion coefficient growing as (ln t)^2, indicating richer dynamics.

Contribution

The study introduces a physically realistic Wind-Tree model and demonstrates it has more diverse superdiffusive regimes than the Lorentz gas, including a previously unobserved (ln t)^2 growth regime.

Findings

Physical Wind-Tree model exhibits superdiffusive regimes beyond Lorentz gas.

Identifies a new superdiffusive regime with D(t)~(ln t)^2.

Wind-Tree model's dynamics are richer and more complex.

Abstract

We consider a physical Ehrenfests' Wind-Tree model where a moving particle is a hard ball rather than (mathematical) point particle. We demonstrate that a physical periodic Wind-Tree model is dynamically richer than a physical or mathematical periodic Lorentz gas. Namely, the physical Wind-Tree model may have diffusive behavior as the Lorentz gas does, but it has more superdiffusive regimes than the Lorentz gas. The new superdiffusive regime where the diffusion coefficient D(t)~(ln t)^2 of dynamics seems to be never observed before in any model.