273,925 research outputs found

    Shock waves on complex networks

    Get PDF
    Power grids, road maps, and river streams are examples of infrastructural networks which are highly vulnerable to external perturbations. An abrupt local change of load (voltage, traffic density, or water level) might propagate in a cascading way and affect a significant fraction of the network. Almost discontinuous perturbations can be modeled by shock waves which can eventually interfere constructively and endanger the normal functionality of the infrastructure. We study their dynamics by solving the Burgers equation under random perturbations on several real and artificial directed graphs. Even for graphs with a narrow distribution of node properties (e.g., degree or betweenness), a steady state is reached exhibiting a heterogeneous load distribution, having a difference of one order of magnitude between the highest and average loads. Unexpectedly we find for the European power grid and for finite Watts-Strogatz networks a broad pronounced bimodal distribution for the loads. To identify the most vulnerable nodes, we introduce the concept of node-basin size, a purely topological property which we show to be strongly correlated to the average load of a node

    Topological Properties of Citation and Metabolic Networks

    Full text link
    Topological properties of "scale-free" networks are investigated by determining their spectral dimensions dSd_S, which reflect a diffusion process in the corresponding graphs. Data bases for citation networks and metabolic networks together with simulation results from the growing network model \cite{barab} are probed. For completeness and comparisons lattice, random, small-world models are also investigated. We find that dSd_S is around 3 for citation and metabolic networks, which is significantly different from the growing network model, for which dSd_S is approximately 7.5. This signals a substantial difference in network topology despite the observed similarities in vertex order distributions. In addition, the diffusion analysis indicates that whereas the citation networks are tree-like in structure, the metabolic networks contain many loops.Comment: 11 pages, 3 figure

    Holographic coherent states from random tensor networks

    Full text link
    Random tensor networks provide useful models that incorporate various important features of holographic duality. A tensor network is usually defined for a fixed graph geometry specified by the connection of tensors. In this paper, we generalize the random tensor network approach to allow quantum superposition of different spatial geometries. We set up a framework in which all possible bulk spatial geometries, characterized by weighted adjacent matrices of all possible graphs, are mapped to the boundary Hilbert space and form an overcomplete basis of the boundary. We name such an overcomplete basis as holographic coherent states. A generic boundary state can be expanded on this basis, which describes the state as a superposition of different spatial geometries in the bulk. We discuss how to define distinct classical geometries and small fluctuations around them. We show that small fluctuations around classical geometries define "code subspaces" which are mapped to the boundary Hilbert space isometrically with quantum error correction properties. In addition, we also show that the overlap between different geometries is suppressed exponentially as a function of the geometrical difference between the two geometries. The geometrical difference is measured in an area law fashion, which is a manifestation of the holographic nature of the states considered.Comment: 33 pages, 8 figures. An error corrected on page 14. Reference update

    Microwave Experiments on Graphs Simulating Spin-1/2 System

    Get PDF
    In this work I study the statistical properties of the Gaussian symplectic ensemble (GSE) by means of microwave experiments on quantum graphs mimicking spin-1/2 systems. Additionally, the transport property of three terminal microwave graphs with orthogonal, unitary and symplectic symmetry is investigated. In the first part of this thesis, following the spirit of the idea proposed by Joyner et al. we construct microwave quantum graphs to realize a antiunitary symmetry T that squares to minus one, T^2 = -1. This symmetry induces degenerate eigenvalues, which are called Kramers doublets. If the classical dynamics of the system is chaotic, statistical features of the spectrum can be well described by the corresponding statistics of random matrix Gaussian symplectic ensemble. Indeed, Kramers doublets are observed in reflection spectrum as expected from the scattering properties of a symplectic graph. The level spacing distribution of these doublets is compared with the corresponding random matrix predictions. Since the level spacing distribution accounts for the short range eigenvalue correlation, to study the spectral long range correlation the spectral two point correlation function and its Fourier transform, the spectral form factor are analyzed. In order to further examine the fluctuation of the eigenvalues smoothed quantities such as number variance and spectral rigidity are discussed. The graphs used in the experiment consist of two subgraphs coupled via one pair of connecting bonds. Theoretical study shows that the level spacing distribution for graphs with one pair of connecting bonds deviates by few percents from the random matrix prediction. This difference is too small to be resolved in the experiment. The one pair of bonds approximation is introduced to better understand the symplectic graph we used in the experiment. This model is extended to address more general cases of the symplectic graph. Finally, the parameter dependent dynamical transition of the statistical features of the spectrum from GSE via Gaussian unitary ensemble (GUE) to Gaussian orthogonal ensemble (GOE) is studied. In the second part of this thesis, the collaborative work with Dr. A. M. MartĂ­nez- ArgĂĽello from Mexico is briefly presented. A three terminal setup is proposed to study the universal transport properties of systems with orthogonal, unitary and symplectic symmetry. The probability distribution for a transport related quantity is predicted analytically and microwave graphs are constructed to test this prediction. The absorption within the system is modeled by effective Hamiltonian approach. The parameters of the absorption and coupling are extracted from the experimental autocorrelation function. This allowed a comparison between experiment and theory without any free parameters. Finally, a quantitative good agreement between experiment and theory was found for all three symmetry classes
    • …
    corecore