Fast algorithm for detecting community structure in networks

It has been found that many networks display community structure -- groups of vertices within which connections are dense but between which they are sparser -- and highly sensitive computer algorithms have in recent years been developed for detecting such structure. These algorithms however are computationally demanding, which limits their application to small networks. Here we describe a new algorithm which gives excellent results when tested on both computer-generated and real-world networks and is much faster, typically thousands of times faster than previous algorithms. We give several example applications, including one to a collaboration network of more than 50000 physicists.Comment: 5 pages, 4 figure

Is a single photon's wave front observable?

The ultimate goal and the theoretical limit of weak signal detection is the ability to detect a single photon against a noisy background. [...] In this paper we show, that a combination of a quantum metamaterial (QMM)-based sensor matrix and quantum non-demolition (QND) readout of its quantum state allows, in principle, to detect a single photon in several points, i.e., to observe its wave front. Actually, there are a few possible ways of doing this, with at least one within the reach of current experimental techniques for the microwave range. The ability to resolve the quantum-limited signal from a remote source against a much stronger local noise would bring significant advantages to such diverse fields of activity as, e.g., microwave astronomy and missile defence. The key components of the proposed method are 1) the entangling interaction of the incoming photon with the QMM sensor array, which produces the spatially correlated quantum state of the latter, and 2) the QND readout of the collective observable (e.g., total magnetic moment), which characterizes this quantum state. The effects of local noise (e.g., fluctuations affecting the elements of the matrix) will be suppressed relative to the signal from the spatially coherent field of (even) a single photon.Comment: 13 pages, 4 figure

Tunable refraction in a two dimensional quantum metamaterial

In this paper we consider a two-dimensional metamaterial comprising an array of qubits (two level quantum objects). Here we show that a two-dimensional quantum metamaterial may be controlled, e.g. via the application of a magnetic flux, so as to provide controllable refraction of an input signal. Our results are consistent with a material that could be quantum birefringent (beam splitter) or not dependent on the application of this control parameter. We note that quantum metamaterials as proposed here may be fabricated from a variety of current candidate technologies from superconducting qubits to quantum dots. Thus the ideas proposed in this work would be readily testable in existing state of the art laboratories.Comment: 4 pages, 2 figure

Correlation, Network and Multifractal Analysis of Global Financial Indices

We apply RMT, Network and MF-DFA methods to investigate correlation, network and multifractal properties of 20 global financial indices. We compare results before and during the financial crisis of 2008 respectively. We find that the network method gives more useful information about the formation of clusters as compared to results obtained from eigenvectors corresponding to second largest eigenvalue and these sectors are formed on the basis of geographical location of indices. At threshold 0.6, indices corresponding to Americas, Europe and Asia/Pacific disconnect and form different clusters before the crisis but during the crisis, indices corresponding to Americas and Europe are combined together to form a cluster while the Asia/Pacific indices forms another cluster. By further increasing the value of threshold to 0.9, European countries France, Germany and UK constitute the most tightly linked markets. We study multifractal properties of global financial indices and find that financial indices corresponding to Americas and Europe almost lie in the same range of degree of multifractality as compared to other indices. India, South Korea, Hong Kong are found to be near the degree of multifractality of indices corresponding to Americas and Europe. A large variation in the degree of multifractality in Egypt, Indonesia, Malaysia, Taiwan and Singapore may be a reason that when we increase the threshold in financial network these countries first start getting disconnected at low threshold from the correlation network of financial indices. We fit Binomial Multifractal Model (BMFM) to these financial markets.Comment: 32 pages, 25 figures, 1 tabl

Persistent entanglement in two coupled SQUID rings in the quantum to classical transition - A quantum jumps approach

We explore the quantum-classical crossover of two coupled, identical, superconducting quantum interference device (SQUID) rings. The motivation for this work is based on a series of recent papers. In ~[1] we showed that the entanglement characteristics of chaotic and periodic (entrained) solutions of the Duffing oscillator differed significantly and that in the classical limit entanglement was preserved only in the chaotic-like solutions. However, Duffing oscillators are a highly idealised toy system. Motivated by a wish to explore more experimentally realisable systems we extended our work in [2,3] to an analysis of SQUID rings. In [3] we showed that the two systems share a common feature. That is, when the SQUID ring's trajectories appear to follow (semi) classical orbits entanglement persists. Our analysis in[3] was restricted to the quantum state diffusion unravelling of the master equation - representing unit efficiency heterodyne detection (or ambi-quadrature homodyne detection). Here we show that very similar behaviour occurs using the quantum jumps unravelling of the master equation. Quantum jumps represents a discontinuous photon counting measurement process. Hence, the results presented here imply that such persistent entanglement is independent of measurement process and that our results may well be quite general in nature.Comment: 6 pages, 3 figures. Published as part of a special issue for the 11th International Conference on Squeezed States and Uncertainty Relations/4th Feynman festival in Olomouc 2009 (This paper extends the results presented in arXiv:0909.4488

A Bright Solitonic Matter-Wave Interferometer

We present the first realisation of a solitonic atom interferometer. A Bose-Einstein condensate of $1\times10^4$ atoms of rubidium-85 is loaded into a horizontal optical waveguide. Through the use of a Feshbach resonance, the $s$-wave scattering length of the $^{85}$Rb atoms is tuned to a small negative value. This attractive atomic interaction then balances the inherent matter-wave dispersion, creating a bright solitonic matter wave. A Mach-Zehnder interferometer is constructed by driving Bragg transitions with the use of an optical lattice co-linear with the waveguide. Matter wave propagation and interferometric fringe visibility are compared across a range of $s$-wave scattering values including repulsive, attractive and non-interacting values. The solitonic matter wave is found to significantly increase fringe visibility even compared with a non-interacting cloud.Comment: 6 pages, 4 figure

A quantum sensor: simultaneous precision gravimetry and magnetic gradiometry with a Bose-Einstein condensate

A Bose-Einstein condensate is used as an atomic source for a high precision sensor. A $5\times 10^6$ atom F=1 spinor condensate of $^{87}$Rb is released into free fall for up to $750$ms and probed with a Mach-Zehnder atom interferometer based on Bragg transitions. The Bragg interferometer simultaneously addresses the three magnetic states, $\left| m_f=1,0,-1 \right\rangle$, facilitating a simultaneous measurement of the acceleration due to gravity with an asymptotic precision of $2.1\times 10^{-9}$$\Delta$g/g and the magnetic field gradient to a precision $8$pT/m