Canonical superdiffusion and energy fluctuation divergence

TL;DR

This paper introduces a Hamiltonian-based physical model exhibiting chaotic superdiffusion and energy fluctuation divergence, with analytical formulas for invariant density and Lyapunov exponent, and proves the system's Anosov diffeomorphism properties.

Contribution

It presents a novel Hamiltonian model demonstrating superdiffusion and divergence phenomena, with analytical characterizations and rigorous proofs of its chaotic dynamics.

Findings

Model exhibits chaotic superdiffusion

Invariant density formula derived analytically

Lyapunov exponent calculated explicitly

Abstract

We propose a noble physical model obtained from a Hamiltonian with periodic potential. This model is canonical, reversible and brings about chaotic superdiffusion with energy fluctuation divergence. The analytical formula of invariant density can be obtained in some parameter range. In the range it is proved that the map is Anosov diffeomorphism and the invariant measure is a SRB measure. We calculate the analytical formula of Lyapunov exponent.