APPROACH TO EQUILIBRIUM IN A LATTICE FIELD-THEORY

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INTERMITTENT BEHAVIOR IN NON-LINEAR-HAMILTONIAN SYSTEMS FAR FROM EQUILIBRIUM

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CALCULATION OF RELAXATION FUNCTIONS - A NEW DEVELOPMENT WITHIN THE MORI FORMALISM

The problem of expanding the correlation functions into continued fractions is considered in the light of a Mori-type formalism. First, we examine the techniques available in the literature for extracting the parameters of the Mori chain from the moments; then, on the basis of physical considerations, we provide a new surprisingly simple and efficient technique and discuss its significance. Some examples are given to illustrate the elegance and the convenience of our procedure

ON THE ONSET OF CHAOTIC MOTION IN TERMS OF GENERALIZED LANGEVIN-EQUATIONS

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Further results on the equipartition threshold in large nonlinear Hamiltonian systems: The Fermi-Pasta-Ulam model

The Fermi-Pasta-Ulam \u3b2 model has been studied by integrating numerically the equations of motion for a system of N nonlinearly coupled oscillators with N ranging from 64 to 512. Multimode excitations have been considered as initial conditions; the number \u394n of initially excited modes is such that the ratio \u394n/N is kept constant. We can consider the system as a gas of weakly coupled phonons (normal modes), so that if we keep the ratio \u394n/N constant we find an analogy with the thermodynamical limit of statistical mechanics where the ratio M/V is constant when both the volume V and the number of particles M are increased up to infinity. The relaxation towards stationary states is followed through the time evolution of a suitably defined \u2018\u2018spectral entropy\u2019\u2019 which depends on the shape of the space Fourier spectrum; this spectral entropy is a good equipartition indicator: Strong evidence is reported in favor of the existence of an equipartition threshold. Its persistence at very different values of N is also clearly shown. The main result concerns the occurrence of the threshold at the same value of the energy density (i.e., of the \u2018\u2018control parameter\u2019\u2019) when the number of degrees of freedom is changed. More general initial conditions are also considered and the same result is found using as a control parameter a pseudo-Reynolds-number R: The threshold occurs at the same critical value Rc when N is varied. It turns out that a fully chaotic regime (equipartition) is obtained with an \u2018\u2018average nonlinearity\u2019\u2019 of the system of about 3%

Relaxation to different stationary states in the Fermi-Pasta-Ulam model

The Fermi-Pasta-Ulam model has been studied following the time evolution of the space Fourier spectrum through the numerical integration of the equations of motion for a system of 128 non-linearly coupled oscillators. One-mode and multimode excitations have been considered as initial conditions; in the former case, an approximate analytic technique has been applied to describe the "short-time" behavior of the system, which fits well the experiment. The main result in both cases is the presence of different stationary states towards which the system is evolving: a 1/k2 spectrum (corresponding to the equipartition of energy) or an exponential spectrum can be reached, depending on the value of some parameter, which takes into account the relative weight of the nonlinear to the linear term of the equations of motion