9 research outputs found

    Wavefunction statistics in open chaotic billiards

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    We study the statistical properties of wavefunctions in a chaotic billiard that is opened up to the outside world. Upon increasing the openings, the billiard wavefunctions cross over from real to complex. Each wavefunction is characterized by a phase rigidity, which is itself a fluctuating quantity. We calculate the probability distribution of the phase rigidity and discuss how phase rigidity fluctuations cause long-range correlations of intensity and current density. We also find that phase rigidities for wavefunctions with different incoming wave boundary conditions are statistically correlated.Comment: 4 pages, RevTeX; 1 figur

    Statistical properties of power-law random banded unitary matrices in the delocalization-localization transition regime

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    Power-law random banded unitary matrices (PRBUM), whose matrix elements decay in a power-law fashion, were recently proposed to model the critical statistics of the Floquet eigenstates of periodically driven quantum systems. In this work, we numerically study in detail the statistical properties of PRBUM ensembles in the delocalization-localization transition regime. In particular, implications of the delocalization-localization transition for the fractal dimension of the eigenvectors, for the distribution function of the eigenvector components, and for the nearest neighbor spacing statistics of the eigenphases are examined. On the one hand, our results further indicate that a PRBUM ensemble can serve as a unitary analog of the power-law random Hermitian matrix model for Anderson transition. On the other hand, some statistical features unseen before are found from PRBUM. For example, the dependence of the fractal dimension of the eigenvectors of PRBUM upon one ensemble parameter displays features that are quite different from that for the power-law random Hermitian matrix model. Furthermore, in the time-reversal symmetric case the nearest neighbor spacing distribution of PRBUM eigenphases is found to obey a semi-Poisson distribution for a broad range, but display an anomalous level repulsion in the absence of time-reversal symmetry.Comment: 10 pages + 13 fig

    Googling social interactions : web search engine based social network construction

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    Social network analysis has long been an untiring topic of sociology. However, until the era of information technology, the availability of data, mainly collected by the traditional method of personal survey, was highly limited and prevented large-scale analysis. Recently, the exploding amount of automatically generated data has completely changed the pattern of research. For instance, the enormous amount of data from so-called high-throughput biological experiments has introduced a systematic or network viewpoint to traditional biology. Then, is “high-throughput” sociological data generation possible? Google, which has become one of the most influential symbols of the new Internet paradigm within the last ten years, might provide torrents of data sources for such study in this (now and forthcoming) digital era. We investigate social networks between people by extracting information on the Web and introduce new tools of analysis of such networks in the context of statistical physics of complex systems or socio-physics. As a concrete and illustrative example, the members of the 109th United States Senate are analyzed and it is demonstrated that the methods of construction and analysis are applicable to various other weighted networks
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