arXiv subjects

Dima L. Shepelyansky

Publications and source records attributed to Dima L. Shepelyansky.

At least 55 records · Page 3Linked to original sources

arXiv2019

Dynamical thermalization of interacting fermionic atoms in a Sinai-oscillator trap

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.

cond-mat.quant-gas↗

arXiv2019

Contagion in Bitcoin networks

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 $κ$. We find that the phase transition takes place for $κ<κ_c\approx0.1$ with almost all users going bankrupt. For $κ>0.55$ almost all users remain safe. We find that even on a distance from the critical threshold $κ_c$ 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.

q-fin.TR↗

arXiv2019

Interdependence of sectors of economic activities for world countries from the reduced Google matrix analysis of WTO data

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.

q-fin.TR↗

arXiv2019

Wigner crystal diode

We study the transport properties of a Wigner crystal in one- and two-dimensional asymmetric periodic potential. We show that the Aubry transition takes place above a certain critical amplitude of potential with the sliding and pinned phase below and above the transition. Due to the asymmetry the Aubry pinned phase is characterized by the diode charge transport of the Wigner crystal. We argue that the recent experimental observations of Aubry transition with cold ions and colloidal monolayers can be extended to asymmetric potentials making possible to observe Wigner crystal diode with these physical systems and electrons on liquid helium.

cond-mat.mes-hall↗

arXiv2019

What is the central bank of Wikipedia?

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.

cs.SI↗

arXiv2019

Evaporative cooling and self-thermalization in an open system of interacting fermions

We study depletion dynamics of an open system of weakly interacting fermions with two-body random interactions. In this model fermions are escaping from the high-energy one-particle orbitals, that mimics the evaporation process used in laboratory experiments with neutral atoms to cool them to ultra-low temperatures. It is shown that due to dynamical thermalization the system instantaneously adjusts to the new chemical potential and temperature, so that occupation numbers of the one-particle orbitals always obey the Fermi-Dirac distribution. In this way we are able to describe the evaporation process which leads to a significant cooling of particles remaining inside the system. We also briefly discuss the evaporation process in the SYK black hole model that corresponds to strongly interacting fermions.

cond-mat.quant-gas↗

arXiv2019

Thermoelectricity of cold ions in optical lattices

We study analytically and numerically the thermoelectric properties of cold ions placed in an optical lattice. 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 Frenkel-Kontorova model. We show that this critical amplitude is proportional to the cube of ion density that allows to perform experimental realization of this system at moderate lattice amplitudes. We show that the Aubry phase is characterized by the dimensionless Seebeck coefficient about 50 and the figure of merit being around 8. We propose possible experimental investigations of such system with cold ions and argue that the experiments with electrons on liquid helium surface can also help to understand its unusual properties. The obtained results represent also a challenge for modern methods of quantum chemistry and material science.

cond-mat.quant-gas↗

arXiv2018

Ising-PageRank model of opinion formation on social networks

We propose a new Ising-PageRank model of opinion formation on a social network by introducing an Ising- or spin-like structure of the corresponding Google matrix. Each elector or node of the network has two components corresponding to a red or blue opinion in the society. Also each elector propagates either the red or the blue opinion on the network so that the links between electors are described by two by two matrices favoring one or the other of the two opinions. An elector votes for red or blue depending on the dominance of its red or blue PageRank vector components. We determine the dependence of the final society vote on the fraction of nodes with red (or blue) influence allowing to determine the transition for the election outcome border between the red or blue option. We show that this transition border is significantly affected by the opinion of society elite electors composed of the top PageRank, CheiRank or 2DRank nodes of the network even if the elite fraction is very small. The analytical and numerical studies are preformed for the networks of English Wikipedia 2017 and Oxford University 2006.

physics.soc-ph↗

arXiv2018

Incommensurate standard map

We 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 while 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 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 metal-insulator transition in space while in momentum we have localization similar to the case of 2D Anderson localization. In the case of three incommensurate frequencies of space potential the quantum evolution is characterized by the Anderson transition similar to 3D case of disordered potential. We discuss possible physical systems with such map description including dynamics of comets and dark matter in planetary systems.

nlin.CD↗

arXiv2018

World influence and interactions of universities from Wikipedia networks

We present Wikipedia Ranking of World Universities (WRWU) based on analysis of networks of 24 Wikipedia editions collected in May 2017. With PageRank and CheiRank algorithms we determine ranking of universities averaged over cultural views of these editions. The comparison with the Shanghai ranking gives overlap of 60% for top 100 universities showing that WRWU gives more significance to their historical development. We show that the new reduced Google matrix algorithm allows to determine interactions between leading universities on a scale of ten centuries. This approach also determines the influence of specific universities on world countries. We also compare different cultural views of Wikipedia editions on significance and influence of universities.

cs.SI↗

arXiv2018

Small world of Ulam networks for chaotic Hamiltonian dynamics

We show that the Ulam method applied to dynamical symplectic maps generates Ulam networks which belong to the class of small world networks appearing for social networks of people, actors, power grids, biological networks and Facebook. We analyze the small world properties of Ulam networks on examples of the Chirikov standard map and the Arnold cat map showing that the number of degrees of separation, or the Erdös number, grows logarithmically with the network size for the regime of strong chaos. This growth is related to the Lyapunov instability of chaotic dynamics. The presence of stability islands leads to an algebraic growth of the Erdös number with the network size. We also compare the time scales related with the Erdös number and the relaxation times of the Perron-Frobenius operator showing that they have a different behavior.

nlin.CD↗

arXiv2018

Interactions and influence of world painters from the reduced Google matrix of Wikipedia networks

This study concentrates on extracting painting art history knowledge from the network structure of Wikipedia. Therefore, we construct theoretical networks of webpages representing the hyper-linked structure of articles of 7 Wikipedia language editions. These 7 networks are analyzed to extract the most influential painters in each edition using Google matrix theory. Importance of webpages of over 3000 painters are measured using PageRank algorithm. The most influential painters are enlisted and their ties are studied with the reduced Google matrix analysis. Reduced Google Matrix is a powerful method that captures both direct and hidden interactions between a subset of selected nodes taking into account the indirect links between these nodes via the remaining part of large global network. This method originates from the scattering theory of nuclear and mesoscopic physics and field of quantum chaos. From this study, we show that it is possible to extract from the components of the reduced Google matrix meaningful information on the ties between these painters. For instance, our analysis groups together painters that belong to the same painting movement and shows meaningful ties between painters of different movements. We also determine the influence of painters on world countries using link sensitivity between Wikipedia articles of painters and countries. The reduced Google matrix approach allows to obtain a balanced view of various cultural opinions of Wikipedia language editions. The world countries with the largest number of top painters of selected 7 Wikipedia editions are found to be Italy, France, Russia. We argue that this approach gives meaningful information about art and that it could be a part of extensive network analysis on human knowledge and cultures.

cs.SI↗

arXiv2018

Dynamical decoherence of a qubit coupled to a quantum dot or the SYK black hole

We study the dynamical decoherence of a qubit weakly coupled to a two-body random interaction model (TBRIM) describing a quantum dot of interacting fermions or the Sachdev-Ye-Kitaev (SYK) black hole model. We determine the rates of qubit relaxation and dephasing for regimes of dynamical thermalization of the quantum dot or of quantum chaos in the SYK model. These rates are found to correspond to the Fermi golden rule and quantum Zeno regimes depending on the qubit-fermion coupling strength. An unusual regime is found where these rates are practically independent of TBRIM parameters. We push forward an analogy between TBRIM and quantum small-world networks with an explosive spreading over exponentially large number of states in a finite time being similar to six degrees of separation in small-world social networks. We find that the SYK model has approximately two-three degrees of separation.

cond-mat.str-el↗

arXiv2017

Google matrix of Bitcoin network

We 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.

cs.SI↗

arXiv2017

Analysis of world terror networks from the reduced Google matrix of Wikipedia

We apply the reduced Google matrix method to analyse interactions between 95 terrorist groups and determine their relationships and influence on 64 world countries. This is done on the basis of the Google matrix of the English Wikipedia (2017) composed of 5416537 articles which accumulate a great part of global human knowledge. The reduced Google matrix takes into account the direct and hidden links between a selection of 159 nodes (articles) appearing due to all paths of a random surfer moving over the whole network. As a result we obtain the network structure of terrorist groups and their relations with selected countries. Using the sensitivity of PageRank to a weight variation of specific links we determine the geopolitical sensitivity and influence of specific terrorist groups on world countries. We argue that this approach can find useful application for more extensive and detailed data bases analysis.

cs.SI↗

arXiv2017

Multi-cultural Wikipedia mining of geopolitics interactions leveraging reduced Google matrix analysis

Geopolitics focuses on political power in relation to geographic space. Interactions among world countries have been widely studied at various scales, observing economic exchanges, world history or international politics among others. This work exhibits the potential of Wikipedia mining for such studies. Indeed, Wikipedia stores valuable fine-grained dependencies among countries by linking webpages together for diverse types of interactions (not only related to economical, political or historical facts). We mine herein the Wikipedia networks of several language editions using the recently proposed method of reduced Google matrix analysis. This approach allows to establish direct and hidden links between a subset of nodes that belong to a much larger directed network. Our study concentrates on 40 major countries chosen worldwide. Our aim is to offer a multicultural perspective on their interactions by comparing networks extracted from five different Wikipedia language editions, emphasizing English, Russian and Arabic ones. We demonstrate that this approach allows to recover meaningful direct and hidden links among the 40 countries of interest.

cs.SI↗

arXiv2017

Chaotic zones around rotating small bodies

Small bodies of the Solar system, like asteroids, trans-Neptunian objects, cometary nuclei, planetary satellites, with diameters smaller than one thousand kilometers usually have irregular shapes, often resembling dumb-bells, or contact binaries. The spinning of such a gravitating dumb-bell creates around it a zone of chaotic orbits. We determine its extent analytically and numerically. We find that the chaotic zone swells significantly if the rotation rate is decreased, in particular, the zone swells more than twice if the rotation rate is decreased ten times with respect to the "centrifugal breakup" threshold. We illustrate the properties of the chaotic orbital zones in examples of the global orbital dynamics about asteroid 243 Ida (which has a moon, Dactyl, orbiting near the edge of the chaotic zone) and asteroid 25143 Itokawa.

astro-ph.EP↗

arXiv2017

Kolmogorov turbulence defeated by Anderson localization for a Bose-Einstein condensate in a Sinai-oscillator trap

We study the dynamics of a Bose-Einstein condensate in a Sinai-oscillator trap under a monochromatic driving force. Such a trap is formed by a harmonic potential and a repulsive disk located in the center vicinity corresponding to the first experiments of condensate formation by Ketterle group in 1995. We argue that the external driving allows to model the regime of weak wave turbulence with the Kolmogorov energy flow from low to high energies. We show that in a certain regime of weak driving and weak nonlinearity such a turbulent energy flow is defeated by the Anderson localization that leads to localization of energy on low energy modes. A critical threshold is determined above which the turbulent flow to high energies becomes possible. We argue that this phenomenon can be studied with ultra cold atoms in magneto-optical traps.

cond-mat.quant-gas↗