Transport properties in chaotic and non-chaotic many particles systems

TL;DR

This study compares transport properties in two deterministic models of Brownian motion, one chaotic and one non-chaotic, revealing that chaos does not significantly affect diffusion coefficients but influences relaxation to equilibrium.

Contribution

It demonstrates that chaotic dynamics are not essential for certain transport properties in many-particle systems, challenging assumptions about chaos and diffusion.

Findings

Diffusion coefficients agree with kinetic theory in both models

Velocity correlations are similar despite different dynamics

Relaxation to equilibrium differs based on particle shape and chaos

Abstract

Two deterministic models for Brownian motion are investigated by means of numerical simulations and kinetic theory arguments. The first model consists of a heavy hard disk immersed in a rarefied gas of smaller and lighter hard disks acting as a thermal bath. The second is the same except for the shape of the particles, which is now square. The basic difference of these two systems lies in the interaction: hard core elastic collisions make the dynamics of the disks chaotic whereas that of squares is not. Remarkably, this difference is not reflected in the transport properties of the two systems: simulations show that the diffusion coefficients, velocity correlations and response functions of the heavy impurity are in agreement with kinetic theory for both the chaotic and the non-chaotic model. The relaxation to equilibrium, however, is very sensitive to the kind of interaction. These observations are used to reconsider and discuss some issues connected to chaos, statistical mechanics and diffusion.