1,721,127 research outputs found
Quantum Gibbs distribution from dynamical thermalization in classical nonlinear lattices
Full text linkWe study numerically time evolution in classical lattices with weak or moderate nonlinearity which leads to interactions between linear modes. Our results show that in a certain strength range a moderate nonlinearity generates a dynamical thermalization process which drives the system to the quantum Gibbs distribution of probabilities, or average oscillation amplitudes. The effective dynamical temperature of the lattice varies from large positive to large negative values depending on the energy of the initially excited modes. This quantum Gibbs distribution is drastically different from the usually expected energy equipartition over linear modes corresponding to a regime of classical thermalization. Possible experimental observations of this dynamical thermalization are discussed for cold atoms in optical lattices, nonlinear photonic lattices and optical fiber arrays.Fil: Ermann, Leonardo. Comision Nacional de Energia Atomica. Gerencia Quimica. CAC; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Shepelyansky, Dima L.. Centre National de la Recherche Scientifique; Franci
Incommensurate standard map
Full text linkWe introduce and study the extension of the Chirikov standard map when the kick potential has two and three incommensurate spatial harmonics. This system is called the incommensurate standard map. At small kick amplitudes, the dynamics is bounded by the isolating Kolmogorov-Arnold-Moser surfaces, whereas above a certain kick strength, it becomes unbounded and diffusive. The quantum evolution at small quantum kick amplitudes is somewhat similar to the case of the Aubru-André model studied in mathematics and experiments with cold atoms in a static incommensurate potential. We show that for the quantum map there is also a metalinsulator transition in space whereas in momentum we have localization similar to the case of two-dimensional Anderson localization. In the case of three incommensurate frequencies of the space potential, the quantum evolution is characterized by the Anderson transition similar to the three-dimensional case of the disordered potential. We discuss possible physical systems with such a map description including dynamics of comets and dark matter in planetary systems.Fil: Ermann, Leonardo. Comisión Nacional de Energía Atómica; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Shepelyansky, Dima L.. Université de Toulouse; Franci
Dynamics and thermalization of a Bose-Einstein condensate in a Sinai-oscillator trap
Full text linkWe study numerically the evolution of Bose-Einstein condensate in the Sinai-oscillator trap described by the Gross-Pitaevskii equation in two dimensions. In the absence of interactions, this trap mimics the properties of Sinai billiards where the classical dynamics is chaotic and the quantum evolution is described by generic properties of quantum chaos and random matrix theory. We show that, above a certain border, the nonlinear interactions between atoms lead to the emergence of dynamical thermalization which generates the statistical Bose-Einstein distribution over eigenmodes of the system without interactions. Below the thermalization border, the evolution remains quasi-integrable. Such a Sinai-oscillator trap, formed by the oscillator potential and a repulsive disk located in the vicinity of the center, had been already realized in first experiments with the Bose-Einstein condensate formation by Ketterle group in 1995 and we argue that it can form a convenient test bed for experimental investigations of dynamical of thermalization. Possible links and implications for Kolmogorov turbulence in absence of noise are also discussed.Fil: Ermann, Leonardo. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Comisión Nacional de Energía Atómica; ArgentinaFil: Vergini, Eduardo. Comisión Nacional de Energía Atómica; ArgentinaFil: Shepelyansky, Dima L.. Universite de Toulouse; Francia. Centre National de la Recherche Scientifique; Franci
Jaynes-Cummings model under monochromatic driving
Full text linkWe study analytically and numerically the properties of the Jaynes-Cummings model under monochromatic driving. The analytical results allow us to understand the regime of two branches of multiphoton excitation in the case of close resonance between resonator and driven frequencies. The rotating wave approximation allows us to reduce the description of the original driven model to an effective Jaynes-Cummings model with strong coupling between photons and qubit. The analytical results are in good agreement with the numerical ones even if there are certain deviations between the theory and numerics in the close vicinity of the resonance. We argue that the rich properties of the driven Jaynes-Cummings model represent a new area for experimental investigations with superconducting qubits and other systems.Fil: Ermann, Leonardo. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Comisión Nacional de Energía Atómica; ArgentinaFil: Carlo, Gabriel Gustavo. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Chepelianskii, Alexei D.. Centre National de la Recherche Scientifique; FranciaFil: Shepelyansky, Dima L.. Centre National de la Recherche Scientifique; Franci
Google matrix
Full text linkThe Google matrix G of a directed network is a stochastic square matrix with nonnegative matrix elements and the sum of elements in each column being equal to unity. This matrix describes a Markov chain (Markov, 1906-a) of transitions of a random surfer performing jumps on a network of nodes connected by directed links. The network is characterized by an adjacency matrix Aij with elements Aij=1 if node j points to node i and zero otherwise. The matrix of Markov transitions Sij is constructed from the adjacency matrix Aij by normalization of the sum of column elements to unity and replacing columns with only zero elements (dangling nodes) with equal elements 1/N where N is the matrix size (number of nodes). Then the elements of the Google matrix are defined as Gij=αSij+(1−α)/N.Fil: Ermann, Leonardo. Comisión Nacional de Energía Atómica. Centro Atómico Constituyentes. Gerencia de Investigación y Aplicaciones; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Frahm, Klaus. Universitá Paul Sabatier; FranciaFil: Shepelyansky, Dima. Universitá Paul Sabatier; Franci
Spectral properties of Google matrix of Wikipedia and other networks
Full text linkWe study the properties of eigenvalues and eigenvectors of the Google matrix of the Wikipedia articles hyperlink network and other real networks. With the help of the Arnoldi method, we analyze the distribution of eigenvalues in the complex plane and show that eigenstates with significant eigenvalue modulus are located on well defined network communities. We also show that the correlator between PageRank and CheiRank vectors distinguishes different organizations of information flow on BBC and Le Monde web sites. © 2013 EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg.Fil: Ermann, Leonardo. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Comisión Nacional de Energía Atómica; ArgentinaFil: Frahm, Klaus M.. Universite de Toulouse; FranciaFil: Shepelyansky, Dima L.. Universite de Toulouse; Franci
Google matrix of Bitcoin network
Full text linkWe construct and study the Google matrix of Bitcoin transactions during the time period from the very beginning in 2009 till April 2013. The Bitcoin network has up to a few millions of bitcoin users and we present its main characteristics including the PageRank and CheiRank probability distributions, the spectrum of eigenvalues of Google matrix and related eigenvectors. We find that the spectrum has an unusual circle-type structure which we attribute to existing hidden communities of nodes linked between their members. We show that the Gini coefficient of the transactions for the whole period is close to unity showing that the main part of wealth of the network is captured by a small fraction of users. In global the Google matrix analysis of bitcoin network gives a new understanding of the bitcoin transactions with PageRank and CheiRank characterization of sellers and buyers which are dominant not simply due to the sold/bought volume but also by taking into account if bitcoins are sold to (bought by) other important sellers (buyers).Fil: Ermann, Leonardo. Comision Nacional de Energia Atomica. Gerencia D/area Invest y Aplicaciones No Nucleares. Gerencia de Física (cab). Div.física Teórica; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Frahm, Klaus M.. Universite de Toulouse; Francia. Centre National de la Recherche Scientifique; FranciaFil: Shepelyansky, Dima L.. Universite de Toulouse; Francia. Centre National de la Recherche Scientifique; Franci
Opinion formation driven by PageRank node influence on directed networks
No full textInternational audienceWe study a two states opinion formation model driven by PageRank node influence and report an extensive numerical study on how PageRank affects collective opinion formations in large-scale empirical directed networks. In our model the opinion of a node can be updated by the sum of its neighbor nodes' opinions weighted by the node influence of the neighbor nodes at each step. We consider PageRank probability and its sublinear power as node influence measures and investigate evolution of opinion under various conditions. First, we observe that all networks reach steady state opinion after a certain relaxation time. This time scale is decreasing with the heterogeneity of node influence in the networks. Second, we find that our model shows consensus and non-consensus behavior in steady state depending on types of networks: Web graph, citation network of physics articles, and LiveJournal social network show non-consensus behavior while Wikipedia article network shows consensus behavior. Third, we find that a more heterogeneous influence distribution leads to a more uniform opinion state in the cases of Web graph, Wikipedia, and Livejournal. However, the opposite behavior is observed in the citation network. Finally we identify that a small number of influential nodes can impose their own opinion on significant fraction of other nodes in all considered networks. Our study shows that the effects of heterogeneity of node influence on opinion formation can be significant and suggests further investigations on the interplay between node influence and collective opinion in networks
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