Vito Latora


    Dynamics and Statistical Mechanics of Systems with Long Range Forces

      In collaboration with A. Rapisarda (Univ. di Catania) and S. Ruffo (Univ. di Firenze) we have studied relaxation to the equilibrium, chaotic properties and anomalous diffusion in the HMF (Hamiltonian Mean Field) model. The model describes a system of N fully-coupled rotors and exhibits a second order phase transition from a clustered phase to a homogeneous one as a function of energy. We find strong chaos in correspondence to the phase transition: the largest Lyapunov exponent and the Kolmogorov-Sinai entropy show a peak at the critical energy. This result is valid in the thermodynamic limit and provides a new bridge between Hamiltonian chaos in systems with many degrees of freedom and equilibrium statistical mechanics [PRL98] [PhysD99]. Anomalous diffusion is observed in a transient out-of-equilibrium regime (quasi-stationary states) and for a small range of energy, below the critical one. The superdiffusive behavior of our system is due to Levy walks of single particles and becomes normal at equilibrium, after a relaxation time which diverges with N [PRL99]. The quasi-stationary state is characterized by non-Gaussian velocity distributions [PRE01].

    Kolmogorov-Sinai Entropy-Rate vs. Thermodynamic Entropy in Chaotic Conservative Systems

      This is a project I started in collaboration with M. Baranger (Center for Theoretical Physics, MIT) when I was postdoctorate fellow at MIT. We studied the connections between two quantities, both called entropies and used in two different fields: the entropy of a thermodynamic system S (the entropy of Boltzmann and Clausius), and K, the Kolmogorov-Sinai entropy, defined by the mathematicians to describe the dyamical instabilities of a trajectory in the phase space and to measure chaos. We considered different chaotic conservative systems (for example a gas, or various conservative chaotic maps) started in far-from-equilibrium initial conditions, and we studied the relaxation to equilibrium. The distribution function, initially localized in a particular region of phase space changes of shape: it stretches in some directions and contracts in others, and it bends on itself many times; soon it diffuses all over the phase space becoming a complicate fractal. The occupied volume stays constant because of the Liouville's theorem, though the shape of the distribution has turned into a filamentous structure. Because of this fractalization process the coarse grained entropy S(t) increases linearly in time until the system reaches equilibrium. In [PRL99] we showed, by means of numerical simulations, that the rate of entropy increase dS/dt is equal to K.

    The Edge of Chaos

      This is a collaboration started in 1999 with C. Tsallis (Santa Fe Institute and CBPF, Rio de Janeiro), A. Rapisarda (Univ. di Catania) and M. Baranger (Center for Theoretical Physics, MIT) about the special phenomena happening at the so-called edge of chaos , i.e. at the transition point between a non chaotic and a chaotic phase. This issue has been the subject of much speculation in connection with the self-organization of complex systems and even with Tsallis' non-extensive thermodynamics. In [PLA00] (see also our letter to the Editor of Science [Science03] ) we illustrate with the simplest dissipative system, the logistic map, how to generalize for a system at the edge of chaos important concepts, such as the entropy and the sensitivity to initial conditions.

    My old love: Nuclear Multifragmentation

      Recent experiments in proton-nucleus and nucleus-nucleus collisions at energies around the Fermi energy have revealed the production of nuclear fragments with size distributions exhibiting power laws. These observations have raised the question whether critical phenomena can be explored in the context of heavy-ion collisions. Many are the open problems: nuclei are finite systems with only few hundreds of constituents, while phase transitions are defined in the thermodynamic limit; moreover a nuclear collision is not an equilibrium process. Crical behavior and multifragmentation in nuclear systems has been my main research interest during my Ph.D. Under the supervision of M. Di Toro (Univ. di Catania) and A. Bonasera (LNS Catania), we have developed statistical as well as dynamical models to describe nuclear fragmentation from a microscopical point of view [PRL94] , [PRC95] , [PRL95] , and we have closely collaborated with different experimental groups [PRL96] .