Non-Gaussian features of chaotic Hamiltonian transport

TL;DR

This paper investigates non-Gaussian features in chaotic Hamiltonian transport, focusing on kurtosis and transport coefficients, and identifies the time scale for Markovian behavior in two-dimensional area-preserving maps.

Contribution

It analytically calculates kurtosis and transport coefficients for chaotic maps, revealing non-Gaussian transport features and the onset of Markovian regimes.

Findings

Kurtosis calculated from diffusion and Burnett coefficients.

A characteristic time scale for Markovian regime identified.

Explicit examples illustrating non-Gaussian transport features.

Abstract

Some non-Gaussian aspects of chaotic transport are investigated for a general class of two-dimensional area-preserving maps. Kurtosis, in particular, is calculated from the diffusion and the Burnett coefficients, which are obtained analytically. A characteristic time scale delimiting the onset of the Markovian regime for the master equation is established. Some explicit examples are discussed.