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

Geometric dynamical observables in rare gas crystals

We present a detailed description of how a differential geometric approach to Hamiltonian dynamics can be used for determining the existence of a crossover between different dynamical regimes in a realistic system, a model of a rare gas solid. Such a geometric approach allows to locate the energy threshold between weakly and strongly chaotic regimes, and to estimate the largest Lyapunov exponent. We show how standard mehods of classical statistical mechanics, i.e. Monte Carlo simulations, can be used for our computational purposes. Finally we consider a Lennard Jones crystal modeling solid Xenon. The value of the energy threshold turns out to be in excellent agreement with the numerical estimate based on the crossover between slow and fast relaxation to equilibrium obtained in a previous work by molecular dynamics simulations.Comment: RevTeX, 19 pages, 6 PostScript figures, submitted to Phys. Rev.

Negative Temperature States in the Discrete Nonlinear Schroedinger Equation

We explore the statistical behavior of the discrete nonlinear Schroedinger equation. We find a parameter region where the system evolves towards a state characterized by a finite density of breathers and a negative temperature. Such a state is metastable but the convergence to equilibrium occurs on astronomical time scales and becomes increasingly slower as a result of a coarsening processes. Stationary negative-temperature states can be experimentally generated via boundary dissipation or from free expansions of wave packets initially at positive temperature equilibrium.Comment: 4 pages, 5 figure

Energy diffusion in hard-point systems

We investigate the diffusive properties of energy fluctuations in a one-dimensional diatomic chain of hard-point particles interacting through a square--well potential. The evolution of initially localized infinitesimal and finite perturbations is numerically investigated for different density values. All cases belong to the same universality class which can be also interpreted as a Levy walk of the energy with scaling exponent 3/5. The zero-pressure limit is nevertheless exceptional in that normal diffusion is found in tangent space and yet anomalous diffusion with a different rate for perturbations of finite amplitude. The different behaviour of the two classes of perturbations is traced back to the "stable chaos" type of dynamics exhibited by this model. Finally, the effect of an additional internal degree of freedom is investigated, finding that it does not modify the overall scenarioComment: 16 pages, 15 figure

Coherent Manipulation of Orbital Feshbach Molecules of Two-Electron Atoms

Ultracold molecules have experienced increasing attention in recent years. Compared to ultracold atoms, they possess several unique properties that make them perfect candidates for the implementation of new quantum-technological applications in several fields, from quantum simulation to quantum sensing and metrology. In particular, ultracold molecules of two-electron atoms (such as strontium or ytterbium) also inherit the peculiar properties of these atomic species, above all the possibility to access metastable electronic states via direct excitation on optical clock transitions with ultimate sensitivity and accuracy. In this paper we report on the production and coherent manipulation of molecular bound states of two fermionic $^{173}$Yb atoms in different electronic (orbital) states $^1$S$_0$ and $^3$P$_0$ in proximity of a scattering resonance involving atoms in different spin and electronic states, called orbital Feshbach resonance. We demonstrate that orbital molecules can be coherently photoassociated starting from a gas of ground-state atoms in a three-dimensional optical lattices by observing several photoassociation and photodissociation cycles. We also show the possibility to coherently control the molecular internal state by using Raman-assisted transfer to swap the nuclear spin of one of the atoms forming the molecule, thus demonstrating a powerful manipulation and detection tool of these molecular bound states. Finally, by exploiting this peculiar detection technique we provide first information on the lifetime of the molecular states in a many-body setting, paving the way towards future investigations of strongly interacting Fermi gases in a still unexplored regime.Comment: 11 pages, 8 figure

A strongly interacting gas of two-electron fermions at an orbital Feshbach resonance

We report on the experimental observation of a strongly interacting gas of ultracold two-electron fermions with orbital degree of freedom and magnetically tunable interactions. This realization has been enabled by the demonstration of a novel kind of Feshbach resonance occurring in the scattering of two 173Yb atoms in different nuclear and electronic states. The strongly interacting regime at resonance is evidenced by the observation of anisotropic hydrodynamic expansion of the two-orbital Fermi gas. These results pave the way towards the realization of new quantum states of matter with strongly correlated fermions with orbital degree of freedom.Comment: 5 pages, 4 figure

Chronic neural probe for simultaneous recording of single-unit, multi-unit, and local field potential activity from multiple brain sites

Drug resistant focal epilepsy can be treated by resecting the epileptic focus requiring a precise focus localization using stereoelectroencephalography (SEEG) probes. As commercial SEEG probes offer only a limited spatial resolution, probes of higher channel count and design freedom enabling the incorporation of macro and microelectrodes would help increasing spatial resolution and thus open new perspectives for investigating mechanisms underlying focal epilepsy and its treatment. This work describes a new fabrication process for SEEG probes with materials and dimensions similar to clinical probes enabling recording single neuron activity at high spatial resolution. Polyimide is used as a biocompatible flexible substrate into which platinum electrodes and leads are... The resulting probe features match those of clinically approved devices. Tests in saline solution confirmed the probe stability and functionality. Probes were implanted into the brain of one monkey (Macaca mulatta), trained to perform different motor tasks. Suitable configurations including up to 128 electrode sites allow the recording of task-related neuronal signals. Probes with 32 and 64 electrode sites were implanted in the posterior parietal cortex. Local field potentials and multi-unit activity were recorded as early as one hour after implantation. Stable single-unit activity was achieved for up to 26 days after implantation of a 64-channel probe. All recorded signals showed modulation during task execution. With the novel probes it is possible to record stable biologically relevant data over a time span exceeding the usual time needed for epileptic focus localization in human patients. This is the first time that single units are recorded along cylindrical polyimide probes chronically implanted 22 mm deep into the brain of a monkey, which suggests the potential usefulness of this probe for human applications

Investigating Echo-State Networks Dynamics by Means of Recurrence Analysis

This is the author accepted manuscript. The final version is available from IEEE via the DOI in this record.In this paper, we elaborate over the well-known interpretability issue in echo-state networks (ESNs). The idea is to investigate the dynamics of reservoir neurons with time-series analysis techniques developed in complex systems research. Notably, we analyze time series of neuron activations with recurrence plots (RPs) and recurrence quantification analysis (RQA), which permit to visualize and characterize high-dimensional dynamical systems. We show that this approach is useful in a number of ways. First, the 2-D representation offered by RPs provides a visualization of the high-dimensional reservoir dynamics. Our results suggest that, if the network is stable, reservoir and input generate similar line patterns in the respective RPs. Conversely, as the ESN becomes unstable, the patterns in the RP of the reservoir change. As a second result, we show that an RQA measure, called Lmax, is highly correlated with the well-established maximal local Lyapunov exponent. This suggests that complexity measures based on RP diagonal lines distribution can quantify network stability. Finally, our analysis shows that all RQA measures fluctuate on the proximity of the so-called edge of stability, where an ESN typically achieves maximum computational capability. We leverage on this property to determine the edge of stability and show that our criterion is more accurate than two well-known counterparts, both based on the Jacobian matrix of the reservoir. Therefore, we claim that RPs and RQA-based analyses are valuable tools to design an ESN, given a specific problem

Boltzmann-Gibbs thermal equilibrium distribution for classical systems and Newton law: A computational discussion

We implement a general numerical calculation that allows for a direct comparison between nonlinear Hamiltonian dynamics and the Boltzmann-Gibbs canonical distribution in Gibbs $\Gamma$-space. Using paradigmatic first-neighbor models, namely, the inertial XY ferromagnet and the Fermi-Pasta-Ulam $\beta$-model, we show that at intermediate energies the Boltzmann-Gibbs equilibrium distribution is a consequence of Newton second law (${\mathbf F}=m{\mathbf a}$). At higher energies we discuss partial agreement between time and ensemble averages.Comment: New title, revision of the text. EPJ latex, 4 figure