Covariant hydrodynamic Lyapunov modes and strong stochasticity threshold in Hamiltonian lattices

TL;DR

This paper demonstrates that covariant Lyapunov vectors reliably identify hydrodynamic modes in Hamiltonian lattices regardless of chaos strength, challenging previous beliefs that strong chaos is necessary.

Contribution

It clarifies the reliability of covariant Lyapunov vectors over Gram-Schmidt vectors for detecting hydrodynamic modes across different chaos regimes.

Findings

Covariant Lyapunov vectors detect HLMs at all energy densities.

Gram-Schmidt vectors can mislead in weak chaos regimes.

Strong chaos is not required for the existence of genuine HLMs.

Abstract

We scrutinize the reliability of covariant and Gram-Schmidt Lyapunov vectors for capturing hydrodynamic Lyapunov modes (HLMs) in one-dimensional Hamiltonian lattices. We show that,in contrast with previous claims, HLMs do exist for any energy density, so that strong chaos is not essential for the appearance of genuine (covariant) HLMs. In contrast, Gram-Schmidt Lyapunov vectors lead to misleading results concerning the existence of HLMs in the case of weak chaos.