The Library of Babel, described by Jorge Luis Borges, stores an enormous amount of information. The Library exists 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. PACS. 89.75.Fb Structures and organization in complex systems -89.75.Hc Networks and genealogical trees -89.20.Hh World Wide Web, Internet

We study analytically and numerically the properties of one-dimensional chain of cold ions placed in a periodic potential of optical lattice and global harmonic potential of a trap. In close similarity with the Frenkel-Kontorova model, a transition from sliding to pinned phase takes place with the increase of the optical lattice potential for the density of ions incommensurate with the lattice period. Quantum fluctuations lead to a quantum phase transition and melting of pinned instanton glass phase at large values of dimensional Planck constant. The obtained results are also relevant for a Wigner crystal placed in a periodic potential. PACS numbers: 32.80.Lg, 32.80.Pj, 63.70.+h, 61.44.Fw Nowadays experimental techniques allow to store thousands of cold ions and observe various ordered structures formed by Coulomb repulsion in ion traps [1]. These structures include the one-dimensional (1D) Wigner crystal, zig-zag and helical structures in three dimensions. The Cirac-Zoller proposal of quantum computations with cold trapped ions [2] generated an enormous experimental progress in this field with implementations of quantum algorithms and quantum state preparation with up to 8 qubits [3,4]. In these experiments [3,4] ions form a 1D chain placed in a global harmonic potential which frequency ω determines the eigenfrequencies of chain oscillations being independent of ion charge [5,6]. Highly accurate experimental control of the chain modes allows to perform quantum gates between internal levels of ions. In addition to ion traps, modern laser techniques allow to create periodic optical lattices and store in them thousands of cold atoms (see e.g. [7]). A single ion dynamics in an optical lattice has been also studied experimentally [8]. The combination of these two techniques makes possible to study experimentally the properties of a 1D chain of few tens of ions placed in an optical lattice and a global harmonic potential at ultra low temperatures.In this Letter we analyze the physical properties of such a system and show that it is closely related to the Frenkel-Kontorova Model (FKM) [9] which gives a mathematical description of various physical phenomena including crystal dislocations, commensurateincommensurate phase transitions, epitaxial monolayers on a crystal surface, magnetic chains and fluxon dynamics in Josephson junctions (see [10] and Refs. therein). As in the classical FKM the ion chain exhibits the Aubry analyticity breaking transition [11] when the amplitude of optical potential becomes larger than a certain critical value. Below the critical point the classical chain can slide (oscillate) in the incommensurate optical lattice while above the transition it becomes pinned by the lattice and a large gap opens in the spectrum of phonon excitations. Above the transition the positions of ions form a devil's staircase corresponding to a fractal Cantor set which replaces a continuous Kolmogorov-Arnold-Moser (KAM) curve in the phase space below the transition. According to [11] the FKM ground state is unique ...

We study numerically the behavior of a qubit coupled to a quantum dissipative driven oscillator (resonator). Above a critical coupling strength the qubit rotations become synchronized with the oscillator phase. In the synchronized regime, at certain parameters, the qubit exhibits tunneling between two orientations with a macroscopic change of the number of photons in the resonator. The lifetimes in these metastable states can be enormously large. The synchronization leads to a drastic change of qubit radiation spectrum with the appearance of narrow lines corresponding to recently observed single artificial-atom lasing [O. Astafiev, Nature (London) 449, 588 (2007)].

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Using method of quantum trajectories we study the behavior of two identical or different superconducting qubits coupled to a quantum dissipative driven resonator. Above a critical coupling strength the qubit rotations become synchronized with the driving field phase and their evolution becomes entangled even if two qubits may significantly differ from one another. Such entangled qubits can radiate entangled photons that opens new opportunities for entangled wireless communication in a microwave range.