Synchronization in large directed networks of coupled phase oscillators

We extend recent theoretical approximations describing the transition to synchronization in large undirected networks of coupled phase oscillators to the case of directed networks. We also consider extensions to networks with mixed positive/negative coupling strengths. We compare our theory with numerical simulations and find good agreement

The emergence of coherence in complex networks of heterogeneous dynamical systems

We present a general theory for the onset of coherence in collections of heterogeneous maps interacting via a complex connection network. Our method allows the dynamics of the individual uncoupled systems to be either chaotic or periodic, and applies generally to networks for which the number of connections per node is large. We find that the critical coupling strength at which a transition to synchrony takes place depends separately on the dynamics of the individual uncoupled systems and on the largest eigenvalue of the adjacency matrix of the coupling network. Our theory directly generalizes the Kuramoto model of equal strength, all-to-all coupled phase oscillators to the case of oscillators with more realistic dynamics coupled via a large heterogeneous network.Comment: 4 pages, 1 figure. Published versio

Approximating the largest eigenvalue of network adjacency matrices

The largest eigenvalue of the adjacency matrix of a network plays an important role in several network processes (e.g., synchronization of oscillators, percolation on directed networks, linear stability of equilibria of network coupled systems, etc.). In this paper we develop approximations to the largest eigenvalue of adjacency matrices and discuss the relationships between these approximations. Numerical experiments on simulated networks are used to test our results.Comment: 7 pages, 4 figure

Controlling the dynamics of an open many-body quantum system with localized dissipation

We experimentally investigate the action of a localized dissipative potential on a macroscopic matter wave, which we implement by shining an electron beam on an atomic Bose-Einstein condensate (BEC). We measure the losses induced by the dissipative potential as a function of the dissipation strength observing a paradoxical behavior when the strength of the dissipation exceeds a critical limit: for an increase of the dissipation rate the number of atoms lost from the BEC becomes lower. We repeat the experiment for different parameters of the electron beam and we compare our results with a simple theoretical model, finding excellent agreement. By monitoring the dynamics induced by the dissipative defect we identify the mechanisms which are responsible for the observed paradoxical behavior. We finally demonstrate the link between our dissipative dynamics and the measurement of the density distribution of the BEC allowing for a generalized definition of the Zeno effect. Due to the high degree of control on every parameter, our system is a promising candidate for the engineering of fully governable open quantum systems

Optical evidence for a spin-filter effect in the charge transport of Eu0.6Ca0.4B6Eu_{0.6}Ca_{0.4}B_{6}

We have measured the optical reflectivity $R(\omega)$ of $Eu_{0.6}Ca_{0.4}B_{6}$ as a function of temperature between 1.5 and 300 $K$ and in external magnetic fields up to 7 $T$. The slope at the onset of the plasma edge feature in $R(\omega)$ increases with decreasing temperature and increasing field but the plasma edge itself does not exhibit the remarkable blue shift that is observed in the binary compound $EuB_{6}$. The analysis of the magnetic field dependence of the low temperature optical conductivity spectrum confirms the previously observed exponential decrease of the electrical resistivity upon increasing, field-induced bulk magnetization at constant temperature. In addition, the individual exponential magnetization dependences of the plasma frequency and scattering rate are extracted from the optical data.Comment: submitted to Phys. Rev. Let

Characterizing the dynamical importance of network nodes and links

The largest eigenvalue of the adjacency matrix of the networks is a key quantity determining several important dynamical processes on complex networks. Based on this fact, we present a quantitative, objective characterization of the dynamical importance of network nodes and links in terms of their effect on the largest eigenvalue. We show how our characterization of the dynamical importance of nodes can be affected by degree-degree correlations and network community structure. We discuss how our characterization can be used to optimize techniques for controlling certain network dynamical processes and apply our results to real networks.Comment: 4 pages, 4 figure

Universality Class of the Reversible-Irreversible Transition in Sheared Suspensions

Collections of non-Brownian particles suspended in a viscous fluid and subjected to oscillatory shear at very low Reynolds number have recently been shown to exhibit a remarkable dynamical phase transition separating reversible from irreversible behaviour as the strain amplitude or volume fraction are increased. We present a simple model for this phenomenon, based on which we argue that this transition lies in the universality class of the conserved DP models or, equivalently, the Manna model. This leads to predictions for the scaling behaviour of a large number of experimental observables. Non-Brownian suspensions under oscillatory shear may thus constitute the first experimental realization of an inactive-active phase transition which is not in the universality class of conventional directed percolation.Comment: 4 pages, 2 figures, final versio

Quantum ratchets in dissipative chaotic systems

Using the method of quantum trajectories we study a quantum chaotic dissipative ratchet appearing for particles in a pulsed asymmetric potential in the presence of a dissipative environment. The system is characterized by directed transport emerging from a quantum strange attractor. This model exhibits, in the limit of small effective Planck constant, a transition from quantum to classical behavior, in agreement with the correspondence principle. We also discuss parameter values suitable for implementation of the quantum ratchet effect with cold atoms in optical lattices.Comment: Significant changes: Several text improvements and new results. Figure 2 modified. Figure 4 adde