Diverging fluctuations of the Lyapunov exponents

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.

5 pages, 3 figures; submitted to PRL

References in corpus (6)

• The large deviation approach to statistical mechanics
• Probing rare physical trajectories with Lyapunov weighted dynamics
• Structure of characteristic Lyapunov vectors in spatiotemporal chaos
• Spatiotemporal structure of Lyapunov vectors in chaotic coupled-map lattices
• Structure of characteristic Lyapunov vectors in anharmonic Hamiltonian lattices
• Characteristic Lyapunov vectors in chaotic time-delayed systems

Cited by in corpus (5)

• Large deviations in chaotic systems: exact results and dynamical phase transition
• Faceted patterns and anomalous surface roughening driven by long-term correlated noise
• Dynamics and transport in the boundary-driven dissipative Klein-Gordon chain
• Nonuniversal large-size asymptotics of the Lyapunov exponent in turbulent globally coupled maps
• Remarkable similarities in distributions of dynamical observables in chaotic systems