Dynamic localization of Lyapunov vectors in Hamiltonian lattices

The convergence of the Lyapunov vector toward its asymptotic shape is investigated in two different one-dimensional Hamiltonian lattices: the so-called Fermi-Pasta-Ulam and Phi (4) chains. In both casts, we find an anomalous behavior, i.e., a clear difference from the previously conjectured analogy with the Kardar-Parisi-Zhang equation. The origin of the discrepancy is eventually traced back to the existence of nontrivial long-range correlations both in space and time. As a consequence of this anomaly, we find that, in a Hamiltonian lattice, the largest Lyapunov exponent is affected by stronger finite-size corrections than standard space-time chaos.