564 research outputs found
Logarithmic current fluctuations in non-equilibrium quantum spin chains
We study zero-temperature quantum spin chains which are characterized by a
non-vanishing current. For the XX model starting from the initial state |... +
+ + - - - ...> we derive an exact expression for the variance of the total spin
current. We show that asymptotically the variance exhibits an anomalously slow
logarithmic growth; we also extract the sub-leading constant term. We then
argue that the logarithmic growth remains valid for the XXZ model in the
critical region.Comment: 9 pages, 4 figures, minor alteration
Slow Cooling of an Ising Ferromagnet
A ferromagnetic Ising chain which is endowed with a single-spin-flip Glauber
dynamics is investigated. For an arbitrary annealing protocol, we derive an
exact integral equation for the domain wall density. This integral equation
admits an asymptotic solution in the limit of extremely slow cooling. For
instance, we extract an asymptotic of the density of domain walls at the end of
the cooling procedure when the temperature vanishes. Slow annealing is usually
studied using a Kibble-Zurek argument; in our setting, this argument leads to
approximate predictions which are in good agreement with exact asymptotics.Comment: 6 page
Stochastic Aggregation: Scaling Properties
We study scaling properties of stochastic aggregation processes in one
dimension. Numerical simulations for both diffusive and ballistic transport
show that the mass distribution is characterized by two independent nontrivial
exponents corresponding to the survival probability of particles and monomers.
The overall behavior agrees qualitatively with the mean-field theory. This
theory also provides a useful approximation for the decay exponents, as well as
the limiting mass distribution.Comment: 6 pages, 7 figure
Kinetics of Aggregation-Annihilation Processes
We investigate the kinetics of many-species systems with aggregation of
similar species clusters and annihilation of opposite species clusters. We find
that the interplay between aggregation and annihilation leads to rich kinetic
behaviors and unusual conservation laws. On the mean-field level, an exact
solution for the cluster-mass distribution is obtained. Asymptotically, this
solution exhibits a novel scaling form if the initial species densities are the
same while in the general case of unequal densities the process approaches
single species aggregation. The theoretical predictions are compared with
numerical simulations in 1D, 2D, and 3D. Nontrivial growth exponents
characterize the mass distribution in one dimension.Comment: 12 pages, revtex, 2 figures available upon reques
Infinite-Order Percolation and Giant Fluctuations in a Protein Interaction Network
We investigate a model protein interaction network whose links represent
interactions between individual proteins. This network evolves by the
functional duplication of proteins, supplemented by random link addition to
account for mutations. When link addition is dominant, an infinite-order
percolation transition arises as a function of the addition rate. In the
opposite limit of high duplication rate, the network exhibits giant structural
fluctuations in different realizations. For biologically-relevant growth rates,
the node degree distribution has an algebraic tail with a peculiar rate
dependence for the associated exponent.Comment: 4 pages, 2 figures, 2 column revtex format, to be submitted to PRL 1;
reference added and minor rewording of the first paragraph; Title change and
major reorganization (but no result changes) in response to referee comments;
to be published in PR
Evolving Networks with Multi-species Nodes and Spread in the Number of Initial Links
We consider models for growing networks incorporating two effects not
previously considered: (i) different species of nodes, with each species having
different properties (such as different attachment probabilities to other node
species); and (ii) when a new node is born, its number of links to old nodes is
random with a given probability distribution. Our numerical simulations show
good agreement with analytic solutions. As an application of our model, we
investigate the movie-actor network with movies considered as nodes and actors
as links.Comment: 5 pages, 5 figures, submitted to PR
Live and Dead Nodes
In this paper, we explore the consequences of a distinction between `live'
and `dead' network nodes; `live' nodes are able to acquire new links whereas
`dead' nodes are static. We develop an analytically soluble growing network
model incorporating this distinction and show that it can provide a
quantitative description of the empirical network composed of citations and
references (in- and out-links) between papers (nodes) in the SPIRES database of
scientific papers in high energy physics. We also demonstrate that the death
mechanism alone can result in power law degree distributions for the resulting
network.Comment: 12 pages, 3 figures. To be published in Computational and
Mathematical Organization Theor
Scaling exponents and clustering coefficients of a growing random network
The statistical property of a growing scale-free network is studied based on
an earlier model proposed by Krapivsky, Rodgers, and Redner [Phys. Rev. Lett.
86, 5401 (2001)], with the additional constraints of forbidden of
self-connection and multiple links of the same direction between any two nodes.
Scaling exponents in the range of 1-2 are obtained through Monte Carlo
simulations and various clustering coefficients are calculated, one of which,
, is of order , indicating the network resembles a
small-world. The out-degree distribution has an exponential cut-off for large
out-degree.Comment: six pages, including 5 figures, RevTex 4 forma
Particle Systems with Stochastic Passing
We study a system of particles moving on a line in the same direction.
Passing is allowed and when a fast particle overtakes a slow particle, it
acquires a new velocity drawn from a distribution P_0(v), while the slow
particle remains unaffected. We show that the system reaches a steady state if
P_0(v) vanishes at its lower cutoff; otherwise, the system evolves
indefinitely.Comment: 5 pages, 5 figure
The egalitarian effect of search engines
Search engines have become key media for our scientific, economic, and social
activities by enabling people to access information on the Web in spite of its
size and complexity. On the down side, search engines bias the traffic of users
according to their page-ranking strategies, and some have argued that they
create a vicious cycle that amplifies the dominance of established and already
popular sites. We show that, contrary to these prior claims and our own
intuition, the use of search engines actually has an egalitarian effect. We
reconcile theoretical arguments with empirical evidence showing that the
combination of retrieval by search engines and search behavior by users
mitigates the attraction of popular pages, directing more traffic toward less
popular sites, even in comparison to what would be expected from users randomly
surfing the Web.Comment: 9 pages, 8 figures, 2 appendices. The final version of this e-print
has been published on the Proc. Natl. Acad. Sci. USA 103(34), 12684-12689
(2006), http://www.pnas.org/cgi/content/abstract/103/34/1268
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