Noise-driven Synchronization in Coupled Map Lattices

Synchronization is shown to occur in spatially extended systems under the effect of additive spatio-temporal noise. In analogy to low dimensional systems, synchronized states are observable only if the maximum Lyapunov exponent $\Lambda$ is negative. However, a sufficiently high noise level can lead, in map with finite domain of definition, to nonlinear propagation of information, even in non chaotic systems. In this latter case the transition to synchronization is ruled by a new ingredient : the propagation velocity of information $V_F$. As a general statement, we can affirm that if $V_F$ is finite the time needed to achieve a synchronized trajectory grows exponentially with the system size $L$, while it increases logarithmically with $L$ when, for sufficiently large noise amplitude, $V_F = 0$ .Comment: 11 pages, Latex - 6 EPS Figs - Proceeding LSD 98 (Marseille

Coupled transport in rotor models

Acknowledgement One of us (AP) wishes to acknowledge S. Flach for enlightening discussions about the relationship between the DNLS equation and the rotor model.Peer reviewedPublisher PD

Negative Temperature States in the Discrete Nonlinear Schroedinger Equation

We explore the statistical behavior of the discrete nonlinear Schroedinger equation. We find a parameter region where the system evolves towards a state characterized by a finite density of breathers and a negative temperature. Such a state is metastable but the convergence to equilibrium occurs on astronomical time scales and becomes increasingly slower as a result of a coarsening processes. Stationary negative-temperature states can be experimentally generated via boundary dissipation or from free expansions of wave packets initially at positive temperature equilibrium.Comment: 4 pages, 5 figure

Emergence of chaotic behaviour in linearly stable systems

Strong nonlinear effects combined with diffusive coupling may give rise to unpredictable evolution in spatially extended deterministic dynamical systems even in the presence of a fully negative spectrum of Lyapunov exponents. This regime, denoted as ``stable chaos'', has been so far mainly characterized by numerical studies. In this manuscript we investigate the mechanisms that are at the basis of this form of unpredictable evolution generated by a nonlinear information flow through the boundaries. In order to clarify how linear stability can coexist with nonlinear instability, we construct a suitable stochastic model. In the absence of spatial coupling, the model does not reveal the existence of any self-sustained chaotic phase. Nevertheless, already this simple regime reveals peculiar differences between the behaviour of finite-size and that of infinitesimal perturbations. A mean-field analysis of the truly spatially extended case clarifies that the onset of chaotic behaviour can be traced back to the diffusion process that tends to shift the growth rate of finite perturbations from the quenched to the annealed average. The possible characterization of the transition as the onset of directed percolation is also briefly discussed as well as the connections with a synchronization transition.Comment: 30 pages, 8 figures, Submitted to Journal of Physics

Energy diffusion in hard-point systems

We investigate the diffusive properties of energy fluctuations in a one-dimensional diatomic chain of hard-point particles interacting through a square--well potential. The evolution of initially localized infinitesimal and finite perturbations is numerically investigated for different density values. All cases belong to the same universality class which can be also interpreted as a Levy walk of the energy with scaling exponent 3/5. The zero-pressure limit is nevertheless exceptional in that normal diffusion is found in tangent space and yet anomalous diffusion with a different rate for perturbations of finite amplitude. The different behaviour of the two classes of perturbations is traced back to the "stable chaos" type of dynamics exhibited by this model. Finally, the effect of an additional internal degree of freedom is investigated, finding that it does not modify the overall scenarioComment: 16 pages, 15 figure