1,417 research outputs found

    Ergodic Properties of Microcanonical Observables

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    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

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    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

    Slow energy relaxation and localization in 1D lattices

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    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 NN. A further crossover back to an exponential law is observed only at much longer times (of the order N3N^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 β\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

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    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

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    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