Microscopic chaos and diffusion

TL;DR

This paper explores how microscopic chaos relates to diffusion in particle models, revealing that nonchaotic systems can also diffuse and that periodic orbits help distinguish chaotic from nonchaotic dynamics.

Contribution

It demonstrates that diffusion can occur without microscopic chaos and highlights the role of periodic orbits in analyzing microscopic dynamics through time series.

Findings

Nonchaotic models can exhibit diffusion.

Standard chaos analysis methods are often inadequate.

Periodic orbits help differentiate chaotic from nonchaotic systems.

Abstract

We investigate the connections between microscopic chaos, defined on a dynamical level and arising from collisions between molecules, and diffusion, characterized by a mean square displacement proportional to the time. We use a number of models involving a single particle moving in two dimensions and colliding with fixed scatterers. We find that a number of microscopically nonchaotic models exhibit diffusion, and that the standard methods of chaotic time series analysis are ill suited to the problem of distinguishing between chaotic and nonchaotic microscopic dynamics. However, we show that periodic orbits play an important role in our models, in that their different properties in chaotic and nonchaotic systems can be used to distinguish such systems at the level of time series analysis, and in systems with absorbing boundaries. Our findings are relevant to experiments aimed at verifying the existence of chaoticity and related dynamical properties on a microscopic level in diffusive systems.