Classical transport in a maximally chaotic chain

TL;DR

This paper investigates a lattice model of coupled chaotic maps, demonstrating that microscopic chaos leads to diffusive transport, with exact Lyapunov exponents and ballistic spreading of perturbations.

Contribution

It introduces a specific coupled cat map chain where Lyapunov exponents are exactly determined and links microscopic chaos to macroscopic diffusive transport.

Findings

Perturbations spread ballistically across the chain.

Phase space profiles exhibit large fluctuations due to chaos.

Diffusive transport is directly inferred from microscopic chaos.

Abstract

A model for a lattice of coupled cat maps has been recently introduced. This new and specific choice of the coupling makes the description especially easy and nontrivial quantities as Lyapunov exponents determined exactly. We studied the ergodic property of the dynamics along such a chain for a local perturbation. While the perturbation spreads across a front growing ballistically, the position and momentum profiles show large fluctuations due to chaos leading to diffusive transport in the phase space. It provides an example where the diffusion can be directly inferred from the microscopic chaos.