810 research outputs found
Google matrix of the world trade network
Using the United Nations Commodity Trade Statistics Database
[http://comtrade.un.org/db/] we construct the Google matrix of the world trade
network and analyze its properties for various trade commodities for all
countries and all available years from 1962 to 2009. The trade flows on this
network are classified with the help of PageRank and CheiRank algorithms
developed for the World Wide Web and other large scale directed networks. For
the world trade this ranking treats all countries on equal democratic grounds
independent of country richness. Still this method puts at the top a group of
industrially developed countries for trade in {\it all commodities}. Our study
establishes the existence of two solid state like domains of rich and poor
countries which remain stable in time, while the majority of countries are
shown to be in a gas like phase with strong rank fluctuations. A simple random
matrix model provides a good description of statistical distribution of
countries in two-dimensional rank plane. The comparison with usual ranking by
export and import highlights new features and possibilities of our approach.Comment: 14 pages, 13 figures. More detailed data and high definition figures
are available on the website:
http://www.quantware.ups-tlse.fr/QWLIB/tradecheirank/index.htm
Destruction of Anderson localization by nonlinearity in kicked rotator at different effective dimensions
We study numerically the frequency modulated kicked nonlinear rotator with
effective dimension . We follow the time evolution of the model up
to kicks and determine the exponent of subdiffusive spreading
which changes from to when the dimension changes from to
. All results are obtained in a regime of relatively strong Anderson
localization well below the Anderson transition point existing for . We
explain that this variation of the exponent is different from the usual
dimensional Anderson models with local nonlinearity where drops
with increasing . We also argue that the renormalization arguments proposed
by Cherroret N et al. arXiv:1401.1038 are not valid.Comment: 8 pages, 3 figure
Google matrix analysis of the multiproduct world trade network
Using the United Nations COMTRADE database \cite{comtrade} we construct the
Google matrix of multiproduct world trade between the UN countries and
analyze the properties of trade flows on this network for years 1962 - 2010.
This construction, based on Markov chains, treats all countries on equal
democratic grounds independently of their richness and at the same time it
considers the contributions of trade products proportionally to their trade
volume. We consider the trade with 61 products for up to 227 countries. The
obtained results show that the trade contribution of products is asymmetric:
some of them are export oriented while others are import oriented even if the
ranking by their trade volume is symmetric in respect to export and import
after averaging over all world countries. The construction of the Google matrix
allows to investigate the sensitivity of trade balance in respect to price
variations of products, e.g. petroleum and gas, taking into account the world
connectivity of trade links. The trade balance based on PageRank and CheiRank
probabilities highlights the leading role of China and other BRICS countries in
the world trade in recent years. We also show that the eigenstates of with
large eigenvalues select specific trade communities.Comment: 19 pages, 25 figure
Quantum Gibbs distribution from dynamical thermalization in classical nonlinear lattices
We 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 energy of initially excited modes. This quantum
Gibbs distribution is drastically different from 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.Comment: 15 pages, 12 figures. Small modifs., video abstract 107MB at
http://www.quantware.ups-tlse.fr/dima/video/gibbs2013.mp
Dynamics and thermalization of Bose-Einstein condensate in Sinai oscillator trap
We 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 rst 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.Comment: 11 pages, 14 figures. Final version. Accepted forpublication at Phys.
Rev. A. Additional information available at
http://www.quantware.ups-tlse.fr/QWLIB/sinaioscillator
Spectral properties of Google matrix of Wikipedia and other networks
We 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.Comment: 10 pages, 9 figure
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 and co-workers in 1995. We allow that the external driving allows us 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. This is in a drastic contrast to the random phase approximation leading to energy flow to high 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 ultracold atoms in magneto-optical traps.Fil: Ermann, Leonardo. Consejo Nacional de Investigaciones CientĂficas y TĂ©cnicas; Argentina. ComisiĂłn Nacional de EnergĂa AtĂłmica; ArgentinaFil: Vergini, Eduardo GermĂĄn. ComisiĂłn Nacional de EnergĂa AtĂłmica; ArgentinaFil: Shepelyansky, Dima L.. Centre National de la Recherche Scientifique; Franci
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