Search

We analyze the Google matrix of directed networks of Wikipedia articles related to 8 recent Wikipedia language editions representing different cultures (English, Arabic, German, Spanish, French, Italian, Russian, Chinese). Using the reduced Google matrix algorithm we determine relations and interactions of 23 society concepts and 17 religions represented by their respective articles for each of the 8 editions. The effective Markov transitions are found to be more intense inside the two blocks of society concepts and religions while transitions between the blocks are significantly reduced. We establish 5 poles of influence for society concepts (Law, Society, Communism, Liberalism, Capitalism) as well as 5 poles for religions (Christianity, Islam, Buddhism, Hinduism, Chinese folk religion) and determine how they affect other entries. We compute inter edition correlations for different key quantities providing a quantitative analysis of the differences or the proximity of views of the 8 cultures with respect to the selected society concepts and religions., Comment: 29 pages, 16 figures, additional material available at: https://www.quantware.ups-tlse.fr/QWLIB/wikiconcepts/index.html

We introduce the Ising Network Opinion Formation (INOF) model and apply it for the analysis of networks of 6 Wikipedia language editions. In the model, Ising spins are placed at network nodes/articles and the steady-state opinion polarization of spins is determined from the Monte Carlo iterations in which a given spin orientation is determined by in-going links from other spins. The main consideration is done for opinion confrontation between {\it capitalism, imperialism} (blue opinion) and {\it socialism, communism} (red opinion). These nodes have fixed spin/opinion orientation while other nodes achieve their steady-state opinions in the process of Monte Carlo iterations. We find that the global network opinion favors {\it socialism, communism} for all 6 editions. The model also determines the opinion preferences for world countries and political leaders, showing good agreement with heuristic expectations. We also present results for opinion competition between {\it Christianity} and {\it Islam}, and USA Democratic and Republican parties. We argue that the INOF approach can find numerous applications for directed complex networks., Comment: 24 pages, 18 figures

We introduce and study a random matrix model of Kolmogorov-Zakharov turbulence in a nonlinear purely dynamical finite size system with many degrees of freedom. For the case of a direct cascade the energy and norm pumping takes place at low energy scales with absorption at high energies. For a pumping strength above a certain chaos border a global chaotic attractor appears with a stationary energy flow through a Hamiltonian inertial energy interval. In this regime, the steady-state norm distribution is described by an algebraic decay with an exponent in agreement with the Kolmogorov-Zakharov theory. Below the chaos border the system is located in the quasi-integrable regime similar to the Kolmogorov-Arnold-Moser theory and the turbulence is suppressed. For the inverse cascade the system rapidly enters a strongly nonlinear regime where the weak turbulence description is invalid. We argue that such a dynamical turbulence is generic showing that it is present in other lattice models with disorder and Anderson localization. We point out that such dynamical models can be realized in multimode optical fibers., Comment: 11 pages, 9 figures, update with published version

We extend the opinion formation approach to probe the world influence of economical organizations. Our opinion formation model mimics a battle between currencies within the international trade network. Based on the United Nations Comtrade database, we construct the world trade network for the years of the last decade from 2010 to 2020. We consider different core groups constituted by countries preferring to trade in a specific currency. We will consider principally two core groups, namely, 5 Anglo-Saxon countries which prefer to trade in US dollar and the 11 BRICS+ which prefer to trade in a hypothetical currency, hereafter called BRI, pegged to their economies. We determine the trade currency preference of the other countries via a Monte Carlo process depending on the direct transactions between the countries. The results obtained in the frame of this mathematical model show that starting from year 2014 the majority of the world countries would have preferred to trade in BRI than USD. The Monte Carlo process reaches a steady state with 3 distinct groups: two groups of countries preferring, whatever is the initial distribution of the trade currency preferences, to trade, one in BRI and the other in USD, and a third group of countries swinging as a whole between USD and BRI depending on the initial distribution of the trade currency preferences. We also analyze the battle between USD, EUR and BRI, and present the reduced Google matrix description of the trade relations between the Anglo-Saxon countries and the BRICS+., Comment: 16 pages, 19 figures (including 9 figures present in Appendix section) and 1 table

We consider a model of an intelligent surfer moving on the Ulam network generated by a chaotic dynamics in the Chirikov standard map. This directed network is obtained by the Ulam method with a division of the phase space in cells of fixed size forming the nodes of a Markov chain. The goal quest for this surfer is to determine the network path from an initial node A to a final node B with minimal resistance given by the sum of inverse transition probabilities. We develop an algorithm for the intelligent surfer that allows to perform the quest in a small number of transitions which grows only logarithmically with the network size. The optimal path search is done on a fractal intersection set formed by nodes with small Erd\"os numbers of the forward and inverted networks. The intelligent surfer exponentially outperforms a naive surfer who tries to minimize its phase space distance to the target B. We argue that such an algorithm provides new hints for motion control in chaotic flows., Comment: 11+5 pages, 7+11 figures

During his state visit to China in April 2023, Brazilian President Lula proposed the creation of a trade currency supported by the BRICS countries. Using the United Nations Comtrade database, providing the frame of the world trade network associated to 194 UN countries during the decade 2010 - 2020, we study a mathematical model of influence battle of three currencies, namely, the US dollar, the euro, and such a hypothetical BRICS currency. In this model, a country trade preference for one of the three currencies is determined by a multiplicative factor based on trade flows between countries and their relative weights in the global international trade. The three currency seed groups are formed by 9 eurozone countries for the euro, 5 Anglo-Saxon countries for the US dollar and the 5 BRICS countries for the new proposed currency. The countries belonging to these 3 currency seed groups trade only with their own associated currency whereas the other countries choose their preferred trade currency as a function of the trade relations with their commercial partners. The trade currency preferences of countries are determined on the basis of a Monte Carlo modeling of Ising type interactions in magnetic spin systems commonly used to model opinion formation in social networks. We adapt here these models to the world trade network analysis. The results obtained from our mathematical modeling of the structure of the global trade network show that as early as 2012 about 58 percent of countries would have preferred to trade with the BRICS currency, 23 percent with the euro and 19 percent with the US dollar. Our results announce favorable prospects for a dominance of the BRICS currency in international trade, if only trade relations are taken into account, whereas political and other aspects are neglected., Comment: 18 pages, 3 figures. Appendix: 4 figures and 3 tables

We consider a system of linear oscillators, or quantum states, described by Random Matrix Theory and analyze how its time evolution is affected by a nonlinear perturbation. Our numerical results show that above a certain chaos border a weak or moderate nonlinearity leads to a dynamical thermalization of a finite number of degrees of freedom with energy equipartition over linear eigenmodes as expected from the laws of classical statistical mechanics. The system temperature is shown to change in a broad range from positive to negative values and the dependence of system characteristics on the initial injected energy is determined. Below the chaos border the dynamics is described by the Kolmogorov-Arnold-Moser integrability. Due to universal features of Random Matrix Theory we argue that the obtained results describe the generic properties of its nonlinear perturbation., Comment: 21=5+16 pages, 5 figures + 16 SupMat figures, additional figures/data available at: https://www.quantware.ups-tlse.fr/QWLIB/nonlinrmt/index.html additional material in SupMat (new figure panels with new parameters and new SupMat sections)

From the Bretton Woods agreement in 1944 till the present day, the US dollar has been the dominant currency in the world trade. However, the rise of the Chinese economy led recently to the emergence of trade transactions in Chinese yuan. Here, we analyze mathematically how the structure of the international trade flows would favor a country to trade whether in US dollar or in Chinese yuan. The computation of the trade currency preference is based on the world trade network built from the 2010-2020 UN Comtrade data. The preference of a country to trade in US dollar or Chinese yuan is determined by two multiplicative factors: the relative weight of trade volume exchanged by the country with its direct trade partners, and the relative weight of its trade partners in the global international trade. The performed analysis, based on Ising spin interactions on the world trade network, shows that, from 2010 to present, a transition took place, and the majority of the world countries would have now a preference to trade in Chinese yuan if one only consider the world trade network structure., Comment: The preprint contains 19 pages including 13 pages of supplementary materials, 12 figures (including 7 supplementary figs) and 6 tables

We study numerically, in the framework of the Cooper approach from 1956, mechanisms of pair formation in a model of La-based cuprate superconductors with longer-ranged hopping parameters reported in the literature at different values of center of mass momentum. An efficient numerical method allows to study lattices with more than a million sites. We consider the cases of attractive Hubbard and d-wave type interactions and a repulsive Coulomb interaction. The approach based on a frozen Fermi sea leads to a complex structure of accessible relative momentum states which is very sensitive to the total pair momentum of static or mobile pairs. It is found that interactions with attraction of approximately half of an electronvolt give a satisfactory agreement with experimentally reported results for the critical superconducting temperature and its dependence on hole doping. Ground states exhibit d-wave symmetries for both attractive Hubbard and d-wave interactions which is essentially due to the particular Fermi surface structure and not entirely to an eventual d-wave symmetry of the interaction. We also find pair states created by Coulomb repulsion at excited energies above the Fermi energy and determine the different mechanisms of their formation. In particular, we identify such pairs in a region of negative mass at rather modest excitation energies which is due to a particular band structure., Comment: 20 pages (16 figures) + 7 pages SupMat (17 figures); additional data/raw figures available at: https://www.quantware.ups-tlse.fr/QWLIB/electronpairsforhtc/

Using the United Nations Comtrade database, we perform the Google matrix analysis of the multiproduct World Trade Network (WTN) for the years 2018-2020 comprising the emergence of the COVID-19 as a global pandemic. The applied algorithms -- the PageRank, the CheiRank and the reduced Google matrix -- take into account the multiplicity of the WTN links providing new insights on the international trade comparing to the usual import-export analysis. These algorithms establish new rankings and trade balances of countries and products considering every countries on equal grounds, independently of their wealth, and every products on the basis of their relative exchanged volumes. In comparison with the pre-COVID-19 period, significant changes in these metrics occur for the year 2020 highlighting a major rewiring of the international trade flows induced by the COVID-19 pandemic crisis. We define a new PageRank-CheiRank product trade balance, either export or import oriented, which is significantly perturbed by the pandemic., Comment: 22 pages, 2 tables, 13 figures, 2 appendices

We introduce and study a two-dimensional dissipative nonlinear Anderson pumping model which is characterized by localized or delocalized eigenmodes in a linear regime and in addition includes nonlinearity, dissipation and pumping. We find that above a certain pumping threshold the model has narrow spectral lasing lines generated by isolated clusters of Anderson attractors. With the increase of the pumping, the lasing spectrum is broaden even if narrow lasing peaks are still well present in the localized phase of linear modes. In the metallic phase, the presence of narrow spectral peaks is significantly suppressed. We argue that the model captures main features observed for random lasers., Comment: 5 pages, 5 figures

We study numerically the properties of entanglement of two interacting, or noninteracting, particles evolving in a regime of quantum chaos in the quantum Chirikov standard map. Such pairs can be viewed as interacting, on noninteracting, Einstein-Podolsky-Rosen pairs in a regime of quantum chaos. The analysis is done with such tools as the Loschmidt echo of entanglement and the Poincar\'e recurrences of entanglement in presence of absorption. The obtained results show unusual features of the entropy of entanglement and the spectrum of Schmidt decomposition with their dependence on interactions at different quantum chaos regimes., Comment: 28 pages, 20 figures and 4 pages with 4 figures Supplementary Material

We consider a situation when evolution of an entangled Einstein-Podolsky-Rosen (EPR) pair takes place in a regime of quantum chaos being chaotic in the classical limit. This situation is studied on an example of chaotic pair dynamics described by the quantum Chirikov standard map. The time evolution is reversible even if a presence of small errors breaks time reversal of classical dynamics due to exponential growth of errors induced by exponential chaos instability. However, the quantum evolution remains reversible since a quantum dynamics instability exists only on a logarithmically short Ehrenfest time scale. We show that due to EPR pair entanglement a measurement of one particle at the moment of time reversal breaks exact time reversal of another particle which demonstrates only an approximate time reversibility. This result is interpreted in the framework of the Schmidt decomposition and Feynman path integral formulation of quantum mechanics. The time reversal in this system has already been realized with cold atoms in kicked optical lattices in absence of entanglement and measurements. On the basis of the obtained results we argue that the experimental investigations of time reversal of chaotic EPR pairs is within reach of present cold atom capabilities., Comment: 15 pages, 19 figures

We study numerically and analytically the behavior of classical Yang-Mills color fields in a random one-dimensional potential described by the Anderson model with disorder. Above a certain threshold the nonlinear interactions of Yang-Mills fields lead to chaos and deconfinement of color wavepackets with their subdiffusive spreading in space. The algebraic exponent of the second moment growth in time is found to be in a range of 0.3 to 0.4. Below the threshold color wavepackets remain confined even if a very slow spreading at very long times is not excluded due to subtle nonlinear effects and the Arnold diffusion for the case when initially color packets are located in a close vicinity. In a case of large initial separation of color wavepackets they remain well confined and localized in space. We also present comparison with the behavior of the one-component field model of discrete Anderson nonlinear Schr\"odinger equation with disorder., Comment: 9 pages, 9 figures

Symmetry breaking in topological matter has become in recent years a key concept in condensed matter physics to unveil novel electronic states. In this work, we predict that broken inversion symmetry and strong spin-orbit coupling in trigonal PtBi$_2$ lead to a type-I Weyl semimetal band structure. Transport measurements show an unusually robust low dimensional superconductivity in thin exfoliated flakes up to 126 nm in thickness (with $T_c \sim 275-400$~mK), which constitutes the first report and study of unambiguous superconductivity in a type-I Weyl semimetal. Remarkably, a Berezinskii-Kosterlitz-Thouless transition with $T_\text{BKT} \sim 310$~mK is revealed in up to 60 nm thick flakes, which is nearly an order of magnitude thicker than the rare examples of two-dimensional superconductors exhibiting such a transition. This makes PtBi$_2$ an ideal platform to study low dimensional and unconventional superconductivity in topological semimetals., Comment: to be published in Nano Letters

We use the United Nations COMTRADE database for analysis of the multiproduct world trade network. With this data, considered for years 2012-2018, we determined the world trade impact of the Kernel of EU 9 countries (KEU9), being Austria, Belgium, France, Germany, Italy, Luxembourg, Netherlands, Portugal, Spain, considered as one united country. We apply the advanced Google matrix analysis for investigation of the influence of KEU9 and show that KEU9 takes the top trade network rank positions thus becoming the main player of the world trade being ahead of USA and China. Our network analysis provides additional mathematical grounds in favor of the recent proposal of KEU9 super-union which is based only on historical, political and economy basis.

We study analytically and numerically the properties of Jaynes-Cummings model under monochromatic driving. The analytical results allow to understand the regime of two branches of multi-photon excitation in the case of close resonance between resonator and driven frequencies. The rotating wave approximation allows to reduce the description of original driven model to an effective Jaynes-Cummings model with strong coupling between photons and qubit. The analytical results are in a 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 driven Jaynes-Cummings model represent a new area for experimental investigations with superconducting qubits and other systems., Comment: 10 pages, 15 figures

We present a model of worldwide crisis contagion based on the Google matrix analysis of the world trade network obtained from the UN Comtrade database. The fraction of bankrupted countries exhibits an \textit{on-off} phase transition governed by a bankruptcy threshold $\kappa$ related to the trade balance of the countries. For $\kappa>\kappa_c$, the contagion is circumscribed to less than 10\% of the countries, whereas, for $\kappa<\kappa_c$, the crisis is global with about 90\% of the countries going to bankruptcy. We measure the total cost of the crisis during the contagion process. In addition to providing contagion scenarios, our model allows to probe the structural trading dependencies between countries. For different networks extracted from the world trade exchanges of the last two decades, the global crisis comes from the Western world. In particular, the source of the global crisis is systematically the Old Continent and The Americas (mainly US and Mexico). Besides the economy of Australia, those of Asian countries, such as China, India, Indonesia, Malaysia and Thailand, are the last to fall during the contagion. Also, the four BRIC are among the most robust countries to the world trade crisis., Comment: Main article: 19 pages, 9 figures. Supplementary files: 7 pages, 2 figures, 4 tables, 1 video. Datasets, results, supplementary information, and high quality figures available at this http://perso.utinam.cnrs.fr/~lages/datasets/WTNcrisis/

We study analytically and numerically dynamics and eigenstates of two electrons with Coulomb repulsion on a tight-binding lattice in one and two dimensions. The total energy and momentum of electrons are conserved and we show that for a certain momentum range the dynamics is exactly reduced to an evolution in an effective narrow energy band where the energy conservation forces the two electrons to propagate together through the whole system at moderate or even weak repulsion strength. We argue that such a mechanism of electron pair formation by the repulsive Coulomb interaction is rather generic and that it can be at the origin of unconventional superconductivity in twisted bilayer graphene., Comment: 5 pages + 10 pages supplementary material with 6 + 10 figures additional avi-video files are available at: http://www.quantware.ups-tlse.fr/QWLIB/coulombelectronpairs/

We study analytically and numerically the properties of phonon modes in an ion quantum computer. The ion chain is placed in a harmonic trap with an additional periodic potential which dimensionless amplitude $K$ determines three main phases available for quantum computations: at zero $K$ we have the case of Cirac-Zoller quantum computer, below a certain critical amplitude $KK_c$ ions are in the pinned Aubry phase with a finite frequency gap protecting quantum gates from temperature and other external fluctuations. For the Aubry phase, in contrast to the Cirac-Zoller and KAM phases, the phonon gap remains independent of the number of ions placed in the trap keeping a fixed ion density around the trap center. We show that in the Aubry phase the phonon modes are much better localized comparing to the Cirac-Zoller and KAM cases. Thus in the Aubry phase the recoil pulses lead to local oscillations of ions while in other two phases they spread rapidly over the whole ion chains making them rather sensible to external fluctuations. We argue that the properties of localized phonon modes and phonon gap in the Aubry phase provide advantages for the ion quantum computations in this phase with a large number of ions., Comment: 10 pages, 5 figures in the main text, 8 figures in the appendix. Accepted for publication in Physical Review A

We study analytically and numerically the thermoelectric properties of a chain of cold atoms with dipole-dipole interactions placed in an optical periodic potential. At small potential amplitudes the chain slides freely that corresponds to the Kolmogorov-Arnold-Moser phase of integrable curves of a symplectic map. Above a certain critical amplitude the chain is pinned by the lattice being in the cantori Aubry phase. We show that the Aubry phase is characterized by exceptional thermoelectric properties with the figure of merit ZT = 25 being ten times larger than the maximal value reached in material science experiments. We show that this system is well accessible for magneto-dipole cold atom experiments that opens new prospects for investigations of thermoelectricity., Comment: 8 pages, 11 figures. Accepted for publication in Applied Sciences (MDPI)

We study numerically transport and thermoelectric properties of electrons placed in a two-dimensional (2D) periodic potential. Our results show that the transition from sliding to pinned phase takes place at a certain critical amplitude of lattice potential being similar to the Aubry transition for the one-dimensional Frenkel-Kontorova model. We show that the 2D Aubry pinned phase is characterized by high values of Seebeck coefficient S = 12. At the same time we find that the value of Seebeck coefficient is significantly influenced by the geometry of periodic potential. We discuss possibilities to test the properties of 2D Aubry phase with electrons on a surface of liquid helium., Comment: 9 pages, 9 figures

Directed protein networks with only a few thousand of nodes are rather complex and do not allow to extract easily the effective influence of one protein to another taking into account all indirect pathways via the global network. Furthermore, the different types of activation and inhibition actions between proteins provide a considerable challenge in the frame work of network analysis. At the same time these protein interactions are of crucial importance and at the heart of cellular functioning. We develop the Google matrix analysis of the protein-protein network from the open public database SIGNOR. The developed approach takes into account the bi-functional activation or inhibition nature of interactions between each pair of proteins describing it in the frame work of Ising-spin matrix transitions. We also apply a recently developed linear response theory for the Google matrix which highlights a pathway of proteins whose PageRank probabilities are most sensitive with respect to two proteins selected for the analysis. This group of proteins is analyzed by the reduced Google matrix algorithm which allows to determine the effective interactions between them due to direct and indirect pathways in the global network. We show that the dominating activation or inhibition function of each protein can be characterized by its magnetization. The results of this Google matrix analysis are presented for three examples of selected pairs of proteins. The developed methods work rapidly and efficiently even for networks with several million of nodes and can be applied to various biological networks., Comment: 23 pages, 18 figures, additional material at: http://www.quantware.ups-tlse.fr/QWLIB/google4signornet/

We develop the linear response theory for the Google matrix PageRank algorithm with respect to a general weak perturbation and a numerical efficient and accurate algorithm, called LIRGOMAX algorithm, to compute the linear response of the PageRank with respect to this perturbation. We illustrate its efficiency on the example of the English Wikipedia network with more than 5 millions of articles (nodes). For a group of initial nodes (or simply a pair of nodes) this algorithm allows to identify the effective pathway between initial nodes thus selecting a particular subset of nodes which are most sensitive to the weak perturbation applied to them (injection or pumping at one node and absorption of probability at another node). The further application of the reduced Google matrix algorithm (REGOMAX) allows to determine the effective interactions between the nodes of this subset. General linear response theory already found numerous applications in various areas of science including statistical and mesoscopic physics. Based on these grounds we argue that the developed LIRGOMAX algorithm will find broad applications in the analysis of complex directed networks., Comment: 11 pages, 8 pdf figures; additional material available at: http://www.quantware.ups-tlse.fr/QWLIB/lirgomax

We study numerically the problem of dynamical thermalization of interacting cold fermionic atoms placed in an isolated Sinai-oscillator trap. This system is characterized by a quantum chaos regime for one-particle dynamics. We show that for a many-body system of cold atoms the interactions, with a strength above a certain quantum chaos border given by the Aberg criterion, lead to the Fermi-Dirac distribution and relaxation of many-body initial states to the thermalized state in absence of any contact with a thermostate. We discuss the properties of this dynamical thermalization and its links with the Loschmidt-Boltzmann dispute., Comment: contribution to the Special Issue in memory of Shmuel Fishman to appear at MDPI Condensed Matter journal; 28 pages, 15+1 figs

We construct the Google matrices of bitcoin transactions for all year quarters during the period of January 11, 2009 till April 10, 2013. During the last quarters the network size contains about 6 million users (nodes) with about 150 million transactions. From PageRank and CheiRank probabilities, analogous to trade import and export, we determine the dimensionless trade balance of each user and model the contagion propagation on the network assuming that a user goes bankrupt if its balance exceeds a certain dimensionless threshold $\kappa$. We find that the phase transition takes place for $\kappa<\kappa_c\approx0.1$ with almost all users going bankrupt. For $\kappa>0.55$ almost all users remain safe. We find that even on a distance from the critical threshold $\kappa_c$ the top PageRank and CheiRank users, as a house of cards, rapidly drop to the bankruptcy. We attribute this effect to strong interconnections between these top users which we determine with the reduced Google matrix algorithm. This algorithm allows to establish efficiently the direct and indirect interactions between top PageRank users. We argue that this study models the contagion on real financial networks., Comment: 12 pages, 6 figures. Paper accepted in 2nd Workshop on Blockchain and Smart Contract Technologies (BSCT 2019), workshop satellite of 22nd International Conference on Business Information Systems (BIS 2019)

We apply the recently developed reduced Google matrix algorithm for the analysis of the OECD-WTO world network of economic activities. This approach allows to determine interdependences and interactions of economy sectors of several countries, including China, Russia and USA, properly taking into account the influence of all other world countries and their economic activities. Within this analysis we also obtain the sensitivity of economy sectors and EU countries to petroleum activity sector. We show that this approach takes into account multiplicity of network links with economy interactions between countries and activity sectors thus providing more rich information compared to the usual export-import analysis., Comment: 20 pages, 10 figures, 1 additional figure in Appendix; minor corrections

We analyze the influence and interactions of 60 largest world banks for 195 world countries using the reduced Google matrix algorithm for the English Wikipedia network with 5 416 537 articles. While the top asset rank positions are taken by the banks of China, with China Industrial and Commercial Bank of China at the first place, we show that the network influence is dominated by USA banks with Goldman Sachs being the central bank. We determine the network structure of interactions of banks and countries and PageRank sensitivity of countries to selected banks. We also present GPU oriented code which significantly accelerates the numerical computations of reduced Google matrix.