Diverging fluctuations of the Lyapunov exponents

TL;DR

This paper demonstrates that in one-dimensional Hamiltonian lattices, the diffusion coefficient of the maximum Lyapunov exponent diverges with system size due to long-range correlations, affecting heat transport and scaling behaviors.

Contribution

It reveals the divergence of Lyapunov exponent diffusion coefficients in 1D Hamiltonian lattices and links this to long-range correlations and anomalous transport phenomena.

Findings

Diffusion coefficient of Lyapunov exponent diverges in the thermodynamic limit.

Normal heat transport exhibits stronger divergence, disrupting standard scaling.

Long-range correlations influence the evolution of hydrodynamic modes.

Abstract

We show that in generic one-dimensional Hamiltonian lattices the diffusion coefficient of the maximum Lyapunov exponent diverges in the thermodynamic limit. We trace this back to the long-range correlations associated with the evolution of the hydrodynamic modes. In the case of normal heat transport, the divergence is even stronger, leading to the breakdown of the usual single-function Family-Vicsek scaling ansatz. A similar scenario is expected to arise in the evolution of rough interfaces in the presence of a suitably correlated background noise.