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, $C_{\rm out}$, is of order $10^{-1}$, 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