1,721,003 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
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
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
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
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
Analysis and modeling of directed complex networks for digital and economic ecosystems
No full textLes réseaux complexes sont des données modélisées sous forme de graphes qui émergent de la Nature et des activités humaines. Ils peuvent atteindre de grandes tailles et présenter des structures particulières, seulement partiellement expliquées par des modèles et mesurables par des métriques. Dans cette thèse, nous nous sommes intéressés à la modélisation et à l'étude de réseaux complexes issus d'écosystèmes numériques et économiques. Nous montrons que la formulation sous forme de graphe permet de mettre à profit des méthodes puissantes pour extraire de l'information d'écosystèmes complexes. En première application, nous proposons de modéliser et d'analyser PeeringDB, une base de données où les AS reportent leur présence à des infrastructures publiques, les IXP, dans le but de faciliter leurs interconnections. Les AS sont la granularité la plus grosse pour étudier Internet à l'échelle mondiale : ce sont des organisations comme des fournisseurs d'accès Internet ou des géants du contenu tels que Facebook, Amazon et Netflix. Nous montrons que le réseau bipartite AS-IXP, pondéré et dirigé, est assez expressif pour pouvoir extraire les caractéristiques principales du peering public d'Internet. Ensuite, avec une méthode dérivée des chaînes de Markov connue sous le nom de complément stochastique, nous retrouvons des liens AS-AS qui sont d'intérêt car peu divulgués par les intéressés pour des raisons de compétition. Par analogie avec d'autres réseaux compétitifs présents en biologie comme les réseaux mutualistes-antagonistes, nous montrons que les AS s'organisent autour des IXP de manière régionale et imbriquée, ce qui a des implications concernant la robustesse du réseau. En seconde application, nous nous intéressons au réseau de commerce international d'échange de produit entre pays reporté dans la base de donnée COMTRADE des Nations Unis. Nous montrons la place dominante de l'Union Européenne des 27, et sa version restreinte à 9 membres du noyau dur, à savoir des pays d'Europe occidentale plus proches historiquement, politiquement et économiquement. Avec des outils dérivés de la matrice de Google, nous quantifions à quel point les économies des principaux acteurs internationaux sont dépendantes entre elles et vis-à-vis de secteurs stratégiques comme l'énergie. La comparaison est faite entre cette approche et la description habituelle Import-Export de ce réseau de commerce mondial. Nous montrons que l'analyse de la matrice Google prend en compte la multiplicité des transactions commerciales et met ainsi mieux en évidence l'influence mondiale de pays et de produits spécifiques.Complex networks are data modeled as graphs that emerge from Nature and human activities. They can reach large sizes and present particular structures, only partially explained by models and measurable by metrics. In this thesis, we are interested in the modeling and study of complex networks from digital and economic ecosystems. We show that the graph formulation allows us to use powerful methods to extract information from complex ecosystems. As a first application, we propose to model and analyze PeeringDB, a database where Autonomous Systems (ASes) report their presence to public infrastructures, the Internet Exchange Points (IXPs), in order to facilitate their interconnections. ASes are the coarsest granularity for studying the Internet on a global scale: they are organizations such as Internet Service Providers or content giants such as Facebook, Amazon, and Netflix. We show that the weighted and directed bipartite AS-IXP network is expressive enough to be able to extract the main features of public Internet peering. Then, with a method derived from Markov chains known as stochastic complementation, we find AS-AS links that are of interest because they are poorly disclosed by stakeholders for competitive reasons. By analogy with other competitive networks present in biology such as mutualistic-antagonistic networks, we show that ASes organize themselves around IXPs in a regional and nested manner, which has implications for network robustness. In a second application, we focus on the international trade network of product exchange between countries reported in the United Nations COMTRADE database. We show the dominant place of the European Union of 27, and its restricted version with 9 core members, i.e. Western European countries closer historically, politically and economically. With tools derived from the Google matrix, we quantify the extent to which the economies of the main international players are dependent on each other and on strategic sectors such as energy. The comparison is made between this approach and the usual Import-Export description of this global trade network. We show that the Google matrix analysis takes into account the multiplicity of trade transactions and thus better highlights the global influence of specific countries and products
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