1,580 research outputs found

### Ergodic Properties of Microcanonical Observables

The problem of the existence of a Strong Stochasticity Threshold in the
FPU-beta model is reconsidered, using suitable microcanonical observables of
thermodynamic nature, like the temperature and the specific heat. Explicit
expressions for these observables are obtained by exploiting rigorous methods
of differential geometry. Measurements of the corresponding temporal
autocorrelation functions locate the threshold at a finite value of the energy
density, that results to be indipendent of the number of degrees of freedom.Comment: 19 pages, 6 figure

### Cooling nonlinear lattices toward localisation

We describe the energy relaxation process produced by surface damping on
lattices of classical anharmonic oscillators. Spontaneous emergence of
localised vibrations dramatically slows down dissipation and gives rise to
quasi-stationary states where energy is trapped in the form of a gas of weakly
interacting discrete breathers. In one dimension (1D), strong enough on--site
coupling may yield stretched--exponential relaxation which is reminiscent of
glassy dynamics. We illustrate the mechanism generating localised structures
and discuss the crucial role of the boundary conditions. For two--dimensional
(2D) lattices, the existence of a gap in the breather spectrum causes the
localisation process to become activated. A statistical analysis of the
resulting quasi-stationary state through the distribution of breathers'
energies yield information on their effective interactions.Comment: 10 pages, 11 figure

### 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

### Slow energy relaxation and localization in 1D lattices

We investigate the energy relaxation process produced by thermal baths at
zero temperature acting on the boundary atoms of chains of classical anharmonic
oscillators. Time-dependent perturbation theory allows us to obtain an explicit
solution of the harmonic problem: even in such a simple system nontrivial
features emerge from the interplay of the different decay rates of Fourier
modes. In particular, a crossover from an exponential to an inverse-square-root
law occurs on a time scale proportional to the system size $N$. A further
crossover back to an exponential law is observed only at much longer times (of
the order $N^3$). In the nonlinear chain, the relaxation process is initially
equivalent to the harmonic case over a wide time span, as illustrated by
simulations of the $\beta$ Fermi-Pasta-Ulam model. The distinctive feature is
that the second crossover is not observed due to the spontaneous appearance of
breathers, i.e. space-localized time-periodic solutions, that keep a finite
residual energy in the lattice. We discuss the mechanism yielding such
solutions and also explain why it crucially depends on the boundary conditions.Comment: 16 pages, 6 figure

### Hydrodynamics and the fluctuation theorem

The fluctuation theorem is a pivotal result of statistical physics. It
quantifies the probability of observing fluctuations which are in violation of
the second law of thermodynamics. More specifically, it quantifies the ratio of
the probabilities of observing entropy-producing and entropy-consuming
fluctuations measured over a finite volume and time span in terms of the rate
of entropy production in the system, the measurement volume and time. We study
the fluctuation theorem in computer simulations of planar shear flow. The
simulations are performed employing the method of multiparticle collision
dynamics which captures both thermal fluctuations and hydrodynamic
interactions. The main outcome of our analysis is that the fluctuation theorem
is verified at any averaging time provided that the measurement volume exhibits
a specific dependence on a hydrodynamic time scale.Comment: 4 pages, 3 figures, to appear on Physical Review Letter

### 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

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