On the non-Boltzmannian nature of quasi-stationary states in long-range interacting systems

We discuss the non-Boltzmannian nature of quasi-stationary states in the Hamiltonian Mean Field (HMF) model, a paradigmatic model for long-range interacting classical many-body systems. We present a theorem excluding the Boltzmann-Gibbs exponential weight in Gibbs $\Gamma$-space of microscopic configurations, and comment a paper recently published by Baldovin and Orlandini (2006). On the basis of the points here discussed, the ongoing debate on the possible application, within appropriate limits, of the generalized $q$-statistics to long-range Hamiltonian systems remains open.Comment: 8 pages, 4 figures. New version accepted for publication in Physica

Prediction of anomalous diffusion and algebraic relaxations for long-range interacting systems, using classical statistical mechanics

We explain the ubiquity and extremely slow evolution of non gaussian out-of-equilibrium distributions for the Hamiltonian Mean-Field model, by means of traditional kinetic theory. Deriving the Fokker-Planck equation for a test particle, one also unambiguously explains and predicts striking slow algebraic relaxation of the momenta autocorrelation, previously found in numerical simulations. Finally, angular anomalous diffusion are predicted for a large class of initial distributions. Non Extensive Statistical Mechanics is shown to be unnecessary for the interpretation of these phenomena

Analysis of Self-Organized Criticality in the Olami-Feder-Christensen model and in real earthquakes

We perform a new analysis on the dissipative Olami-Feder-Christensen model on a small world topology considering avalanche size differences. We show that when criticality appears the Probability Density Functions (PDFs) for the avalanche size differences at different times have fat tails with a q-Gaussian shape. This behaviour does not depend on the time interval adopted and is found also when considering energy differences between real earthquakes. Such a result can be analytically understood if the sizes (released energies) of the avalanches (earthquakes) have no correlations. Our findings support the hypothesis that a self-organized criticality mechanism with long-range interactions is at the origin of seismic events and indicate that it is not possible to predict the magnitude of the next earthquake knowing those of the previous ones.Comment: 5 pages, 3 figures. New version accepted for publication on PRE Rapid Communication

Collective Charge Fluctuations in Single-Electron Processes on Nano-Networks

Using numerical modeling we study emergence of structure and structure-related nonlinear conduction properties in the self-assembled nanoparticle films. Particularly, we show how different nanoparticle networks emerge within assembly processes with molecular bio-recognition binding. We then simulate the charge transport under voltage bias via single-electron tunnelings through the junctions between nanoparticles on such type of networks. We show how the regular nanoparticle array and topologically inhomogeneous nanonetworks affect the charge transport. We find long-range correlations in the time series of charge fluctuation at individual nanoparticles and of flow along the junctions within the network. These correlations explain the occurrence of a large nonlinearity in the simulated and experimentally measured current-voltage characteristics and non-Gaussian fluctuations of the current at the electrode.Comment: 10 pages, 7 figure

Lynden-Bell and Tsallis distributions for the HMF model

Systems with long-range interactions can reach a Quasi Stationary State (QSS) as a result of a violent collisionless relaxation. If the system mixes well (ergodicity), the QSS can be predicted by the statistical theory of Lynden-Bell (1967) based on the Vlasov equation. When the initial distribution takes only two values, the Lynden-Bell distribution is similar to the Fermi-Dirac statistics. Such distributions have recently been observed in direct numerical simulations of the HMF model (Antoniazzi et al. 2006). In this paper, we determine the caloric curve corresponding to the Lynden-Bell statistics in relation with the HMF model and analyze the dynamical and thermodynamical stability of spatially homogeneous solutions by using two general criteria previously introduced in the literature. We express the critical energy and the critical temperature as a function of a degeneracy parameter fixed by the initial condition. Below these critical values, the homogeneous Lynden-Bell distribution is not a maximum entropy state but an unstable saddle point. We apply these results to the situation considered by Antoniazzi et al. For a given energy, we find a critical initial magnetization above which the homogeneous Lynden-Bell distribution ceases to be a maximum entropy state, contrary to the claim of these authors. For an energy U=0.69, this transition occurs above an initial magnetization M_{x}=0.897. In that case, the system should reach an inhomogeneous Lynden-Bell distribution (most mixed) or an incompletely mixed state (possibly fitted by a Tsallis distribution). Thus, our theoretical study proves that the dynamics is different for small and large initial magnetizations, in agreement with numerical results of Pluchino et al. (2004). This new dynamical phase transition may reconcile the two communities

Exploring the thermodynamic limit of Hamiltonian models: convergence to the Vlasov equation

We here discuss the emergence of Quasi Stationary States (QSS), a universal feature of systems with long-range interactions. With reference to the Hamiltonian Mean Field (HMF) model, numerical simulations are performed based on both the original $N$-body setting and the continuum Vlasov model which is supposed to hold in the thermodynamic limit. A detailed comparison unambiguously demonstrates that the Vlasov-wave system provides the correct framework to address the study of QSS. Further, analytical calculations based on Lynden-Bell's theory of violent relaxation are shown to result in accurate predictions. Finally, in specific regions of parameters space, Vlasov numerical solutions are shown to be affected by small scale fluctuations, a finding that points to the need for novel schemes able to account for particles correlations.Comment: 5 pages, 3 figure

Weak chaos and metastability in a symplectic system of many long-range-coupled standard maps

We introduce, and numerically study, a system of $N$ symplectically and globally coupled standard maps localized in a $d=1$ lattice array. The global coupling is modulated through a factor $r^{-\alpha}$, being $r$ the distance between maps. Thus, interactions are {\it long-range} (nonintegrable) when $0\leq\alpha\leq1$, and {\it short-range} (integrable) when $\alpha>1$. We verify that the largest Lyapunov exponent $\lambda_M$ scales as $\lambda_{M} \propto N^{-\kappa(\alpha)}$, where $\kappa(\alpha)$ is positive when interactions are long-range, yielding {\it weak chaos} in the thermodynamic limit $N\to\infty$ (hence $\lambda_M\to 0$). In the short-range case, $\kappa(\alpha)$ appears to vanish, and the behaviour corresponds to {\it strong chaos}. We show that, for certain values of the control parameters of the system, long-lasting metastable states can be present. Their duration $t_c$ scales as $t_c \propto N^{\beta(\alpha)}$, where $\beta(\alpha)$ appears to be numerically consistent with the following behavior: $\beta >0$ for $0 \le \alpha < 1$, and zero for $\alpha\ge 1$. All these results exhibit major conjectures formulated within nonextensive statistical mechanics (NSM). Moreover, they exhibit strong similarity between the present discrete-time system, and the $\alpha$-XY Hamiltonian ferromagnetic model, also studied in the frame of NSM.Comment: 8 pages, 5 figure

The new generation of SPAD—Single-Photon Avalanche Diodes arrays

In the last years the single-photon detection with silicon devices has become an important goal. Here we present the performance of a new generation of single-photon avalanche diodes manufactured by ST-Microelectronics. The 5 × 5 array configuration has been also realized and the performances, in terms of crosstalk and common readout mode, have been investigated

Refining rodent models of spinal cord injury.

This report was produced by an Expert Working Group (EWG) consisting of UK-based researchers, veterinarians and regulators of animal experiments with specialist knowledge of the use of animal models of spinal cord injury (SCI). It aims to facilitate the implementation of the Three Rs (Replacement, Reduction and Refinement), with an emphasis on refinement. Specific animal welfare issues were identified and discussed, and practical measures proposed, with the aim of reducing animal use and suffering, reducing experimental variability, and increasing translatability within this critically important research field