1,235 research outputs found
Poisson statistics of PageRank probabilities of Twitter and Wikipedia networks
We use the methods of quantum chaos and Random Matrix Theory for analysis of
statistical fluctuations of PageRank probabilities in directed networks. In
this approach the effective energy levels are given by a logarithm of PageRank
probability at a given node. After the standard energy level unfolding
procedure we establish that the nearest spacing distribution of PageRank
probabilities is described by the Poisson law typical for integrable quantum
systems. Our studies are done for the Twitter network and three networks of
Wikipedia editions in English, French and German. We argue that due to absence
of level repulsion the PageRank order of nearby nodes can be easily
interchanged. The obtained Poisson law implies that the nearby PageRank
probabilities fluctuate as random independent variables.Comment: 4 pages, 4 figures http://www.quantware.ups-tlse.fr
Crossover of magnetoconductance autocorrelation for a ballistic chaotic quantum dot
The autocorrelation function C_{\varphi,\eps}(\Delta\varphi,\,\Delta \eps)=
\langle \delta g(\varphi,\,\eps)\, \delta
g(\varphi+\Delta\varphi,\,\eps+\Delta \eps)\rangle ( and \eps are
rescaled magnetic flux and energy) for the magnetoconductance of a ballistic
chaotic quantum dot is calculated in the framework of the supersymmetric
non-linear -model. The Hamiltonian of the quantum dot is modelled by a
Gaussian random matrix. The particular form of the symmetry breaking matrix is
found to be relevant for the autocorrelation function but not for the average
conductance. Our results are valid for the complete crossover from orthogonal
to unitary symmetry and their relation with semiclassical theory and an
-matrix Brownian motion ensemble is discussed.Comment: 7 pages, no figures, accepted for publication in Europhysics Letter
Emergence of Quantum Ergodicity in Rough Billiards
By analytical mapping of the eigenvalue problem in rough billiards on to a
band random matrix model a new regime of Wigner ergodicity is found. There the
eigenstates are extended over the whole energy surface but have a strongly
peaked structure. The results of numerical simulations and implications for
level statistics are also discussed.Comment: revtex, 4 pages, 4 figure
Conductance length autocorrelation in quasi one-dimensional disordered wires
Employing techniques recently developed in the context of the Fokker--Planck
approach to electron transport in disordered systems we calculate the
conductance length correlation function
for quasi 1d wires. Our result is valid for arbitrary lengths L and .
In the metallic limit the correlation function is given by a squared
Lorentzian. In the localized regime it decays exponentially in both L and
. The correlation length is proportional to L in the metallic regime
and saturates at a value approximately given by the localization length
as .Comment: 23 pages, Revtex, two figure
Properties of the chiral spin liquid state in generalized spin ladders
We study zero temperature properties of a system of two coupled quantum spin
chains subject to fields explicitly breaking time reversal symmetry and parity.
Suitable choice of the strength of these fields gives a model soluble by Bethe
Ansatz methods which allows to determine the complete magnetic phase diagram of
the system and the asymptotics of correlation functions from the finite size
spectrum. The chiral properties of the system for both the integrable and the
nonintegrable case are studied using numerical techniques.Comment: 19 pages, 9eps figures, Late
Localization in a rough billiard: A sigma model formulation
We consider the quantum dynamics of a particle in a weakly rough billiard.
The Floquet operator for reflection at the boundary is obtained as a unitary
band matrix. The resulting dynamics in angular momentum space can be treated in
the framework of the one-dimensional supersymmetric nonlinear sigma model. We
find analytically localization and the corresponding localization length
where is the classical diffusion constant due to boundary
scattering.Comment: 4 pages, Revtex, no figures, to appear in Phys. Rev. B, Rapid
Communication
Undersampled radial MRI with multiple coils. Iterative image reconstruction using a total variation constraint
Localized to extended states transition for two interacting particles in a two-dimensional random potential
We show by a numerical procedure that a short-range interaction induces
extended two-particle states in a two-dimensional random potential. Our
procedure treats the interaction as a perturbation and solve Dyson's equation
exactly in the subspace of doubly occupied sites. We consider long bars of
several widths and extract the macroscopic localization and correlation lengths
by an scaling analysis of the renormalized decay length of the bars. For ,
the critical disorder found is , and the critical
exponent . For two non-interacting particles we do not find any
transition and the localization length is roughly half the one-particle value,
as expected.Comment: 4 two-column pages, 4 eps figures, Revtex, to be published in
Europhys. Let
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