Two-dimensional ranking of Wikipedia articles

The Library of Babel, described by Jorge Luis Borges, stores an enormous amount of information. The Library exists {\it ab aeterno}. Wikipedia, a free online encyclopaedia, becomes a modern analogue of such a Library. Information retrieval and ranking of Wikipedia articles become the challenge of modern society. While PageRank highlights very well known nodes with many ingoing links, CheiRank highlights very communicative nodes with many outgoing links. In this way the ranking becomes two-dimensional. Using CheiRank and PageRank we analyze the properties of two-dimensional ranking of all Wikipedia English articles and show that it gives their reliable classification with rich and nontrivial features. Detailed studies are done for countries, universities, personalities, physicists, chess players, Dow-Jones companies and other categories.Comment: RevTex 9 pages, data, discussion added, more data at http://www.quantware.ups-tlse.fr/QWLIB/2drankwikipedia

How Well a Chaotic Quantum System Can Retain Memory of Its Initial State?

In classical mechanics the local exponential instability effaces the memory of initial conditions and leads to practical irreversibility. In striking contrast, quantum mechanics appears to exhibit strong memory of the initial state. We relate the latter fact to the low (at most linear) rate with which the system's Wigner function gets during evolution more and more complicated structure and establish existence of a critical strength of external influence below which such a memory still survives.Comment: 5 pages, 4 figure

Quantum correlations and synchronization measures

The phenomenon of spontaneous synchronization is universal and only recently advances have been made in the quantum domain. Being synchronization a kind of temporal correlation among systems, it is interesting to understand its connection with other measures of quantum correlations. We review here what is known in the field, putting emphasis on measures and indicators of synchronization which have been proposed in the literature, and comparing their validity for different dynamical systems, highlighting when they give similar insights and when they seem to fail.Comment: book chapter, 18 pages, 7 figures, Fanchini F., Soares Pinto D., Adesso G. (eds) Lectures on General Quantum Correlations and their Applications. Quantum Science and Technology. Springer (2017

Quantum phase transition in the Frenkel-Kontorova chain: from pinned instanton glass to sliding phonon gas

We study analytically and numerically the one-dimensional quantum Frenkel-Kontorova chain in the regime when the classical model is located in the pinned phase characterized by the gaped phonon excitations and devil's staircase. By extensive quantum Monte Carlo simulations we show that for the effective Planck constant $\hbar$ smaller than the critical value $\hbar_c$ the quantum chain is in the pinned instanton glass phase. In this phase the elementary excitations have two branches: phonons, separated from zero energy by a finite gap, and instantons which have an exponentially small excitation energy. At $\hbar=\hbar_c$ the quantum phase transition takes place and for $\hbar>\hbar_c$ the pinned instanton glass is transformed into the sliding phonon gas with gapless phonon excitations. This transition is accompanied by the divergence of the spatial correlation length and appearence of sliding modes at $\hbar>\hbar_c$.Comment: revtex 16 pages, 18 figure

Towards resolution of the scalar meson nonet enigma

By the application of a linear mass spectrum to a composite system of both the pseudoscalar and scalar meson nonets, we find three mass relations for the masses of the scalar states which suggest the $q\bar{q}$ assignment for the scalar meson nonet: $a_0(1320),$ $K_0^\ast (1430),$ $f_0(1500),$ $f_0'(980).$Comment: 16 pages, LaTe

Gell-Mann--Okubo Mass Formula for an SU(4) Meson Hexadecuplet

Using a linear mass spectrum of an $SU(4)$ meson hexadecuplet, we derive the Gell-Mann--Okubo mass formula for the charmed mesons, in good agreement with experiment. Possible generalization of this method to a higher symmetry group is briefly discussed.Comment: 11 pages, LaTe

Wigner crystal in snaked nanochannels

We study properties of Wigner crystal in snaked nanochannels and show that they are characterized by conducting sliding phase at low charge densities and insulating pinned phase emerging above a certain critical charge density. The transition between these phases has a devil's staircase structure typical for the Aubry transition in dynamical maps and the Frenkel-Kontorova model. We discuss implications of this phenomenon for charge density waves in quasi-one-dimensional organic conductors and for supercapacitors in nanopore materials.Comment: 4 pages, 6 figs, research at http://www.quantware.ups-tlse.f