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 cases, 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.
Pikovsky
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Department of Physics, University of Potsdam, Am Neuen Palais, PF 601553, D-14415, Potsdam, Germany.
Politi
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