Time evolution of Wikipedia network ranking

We study the time evolution of ranking and spectral properties of the Google matrix of English Wikipedia hyperlink network during years 2003 - 2011. The statistical properties of ranking of Wikipedia articles via PageRank and CheiRank probabilities, as well as the matrix spectrum, are shown to be stabilized for 2007 - 2011. A special emphasis is done on ranking of Wikipedia personalities and universities. We show that PageRank selection is dominated by politicians while 2DRank, which combines PageRank and CheiRank, gives more accent on personalities of arts. The Wikipedia PageRank of universities recovers 80 percents of top universities of Shanghai ranking during the considered time period.Comment: 10 pages, 11 figures. Accepted for publication in EPJ

Persistent currents in diffusive metallic cavities: Large values and anomalous scaling with disorder

The effect of disorder on confined metallic cavities with an Aharonov-Bohm flux line is addressed. We find that, even deep in the diffusive regime, large values of persistent currents may arise for a wide variety of geometries. We present numerical results supporting an anomalous scaling law of the average typical current $$ with the strength of disorder $w$, $\sim w^{- \gamma}$ with $\gamma < 2$. This is contrasted with previously reported results obtained for cylindrical samples where a scaling $\sim w^{-2}$ has been found. Possible links to, up to date, unexplained experimental data are finally discussed.Comment: 5 pages, 4 figure

Effect of the coupling to a superconductor on the level statistics of a metal grain in a magnetic field

Wetensch. publicatieFaculteit der Wiskunde en Natuurwetenschappe

Quantum limit of the laser line width in chaotic cavities and statistics of residues of scattering matrix poles

Wetensch. publicatieFaculteit der Wiskunde en Natuurwetenschappe

Weak localization and conductance fluctuations of a chaotic quantum dot with tunable spin-orbit coupling

In a two-dimensional quantum dot in a GaAs heterostructure, the spin-orbit scattering rate is substantially reduced below the rate in a bulk two-dimensional electron gas [B.I. Halperin et al, Phys. Rev. Lett. 86, 2106 (2001)]. Such a reduction can be undone if the spin-orbit coupling parameters acquire a spatial dependence, which can be achieved, e.g., by a metal gate covering only a part of the quantum dot. We calculate the effect of such spatially non-uniform spin-orbit scattering on the weak localization correction and the universal conductance fluctuations of a chaotic quantum dot coupled to electron reservoirs by ballistic point contacts, in the presence of a magnetic field parallel to the plane of the quantum dot.Comment: 4 pages, RevTeX; 2 figures. Substantial revision

Level statistics and eigenfunctions of pseudointegrable systems: dependence on energy and genus number

We study the level statistics (second half moment $I_0$ and rigidity $\Delta_3$) and the eigenfunctions of pseudointegrable systems with rough boundaries of different genus numbers $g$. We find that the levels form energy intervals with a characteristic behavior of the level statistics and the eigenfunctions in each interval. At low enough energies, the boundary roughness is not resolved and accordingly, the eigenfunctions are quite regular functions and the level statistics shows Poisson-like behavior. At higher energies, the level statistics of most systems moves from Poisson-like towards Wigner-like behavior with increasing $g$. Investigating the wavefunctions, we find many chaotic functions that can be described as a random superposition of regular wavefunctions. The amplitude distribution $P(\psi)$ of these chaotic functions was found to be Gaussian with the typical value of the localization volume $V_{\rm{loc}}\approx 0.33$. For systems with periodic boundaries we find several additional energy regimes, where $I_0$ is relatively close to the Poisson-limit. In these regimes, the eigenfunctions are either regular or localized functions, where $P(\psi)$ is close to the distribution of a sine or cosine function in the first case and strongly peaked in the second case. Also an interesting intermediate case between chaotic and localized eigenfunctions appears

Influence of Spatial Correlations on the Lasing Threshold of Random Lasers

The lasing threshold of a random laser is computed numerically from a generic model. It is shown that spatial correlations of the disorder in the medium (i.e., dielectric constant) lead to an increase of the decay rates of the eigenmodes and of the lasing threshold. This is in conflict with predictions that such correlations should lower the threshold. While all results are derived for photonic systems, the computed decay rate distributions also apply to electronic systems

Decay Rate Distributions of Disordered Slabs and Application to Random Lasers

We compute the distribution of the decay rates (also referred to as residues) of the eigenstates of a disordered slab from a numerical model. From the results of the numerical simulations, we are able to find simple analytical formulae that describe those results well. This is possible for samples both in the diffusive and in the localised regime. As example of a possible application, we investigate the lasing threshold of random lasers.Comment: 11 pages, 11 figure

Level spacing statistics of classically integrable systems -Investigation along the line of the Berry-Robnik approach-

By extending the approach of Berry and Robnik, the limiting level spacing distribution of a system consisting of infinitely many independent components is investigated. The limiting level spacing distribution is characterized by a single monotonically increasing function $\bar{\mu}(S)$ of the level spacing $S$. Three cases are distinguished: (i) Poissonian if $\bar{\mu}(+\infty)=0$, (ii) Poissonian for large $S$, but possibly not for small $S$ if $0<\bar{\mu}(+\infty)< 1$, and (iii) sub-Poissonian if $\bar{\mu}(+\infty)=1$. This implies that, even when energy-level distributions of individual components are statistically independent, non-Poissonian level spacing distributions are possible.Comment: 19 pages, 4 figures. Accepted for publication in Phys. Rev.

Weak localization of disordered quasiparticles in the mixed superconducting state

Starting from a random matrix model, we construct the low-energy effective field theory for the noninteracting gas of quasiparticles of a disordered superconductor in the mixed state. The theory is a nonlinear sigma model, with the order parameter field being a supermatrix whose form is determined solely on symmetry grounds. The weak localization correction to the field-axis thermal conductivity is computed for a dilute array of s-wave vortices near the lower critical field H_c1. We propose that weak localization effects, cut off at low temperatures by the Zeeman splitting, are responsible for the field dependence of the thermal conductivity seen in recent high-T_c experiments by Aubin et al.Comment: RevTex, 8 pages, 1 eps figure, typos correcte