71,735 research outputs found

### Representation of SO(3) Group by a Maximally Entangled State

A representation of the SO(3) group is mapped into a maximally entangled two
qubit state according to literatures. To show the evolution of the entangled
state, a model is set up on an maximally entangled electron pair, two electrons
of which pass independently through a rotating magnetic field. It is found that
the evolution path of the entangled state in the SO(3) sphere breaks an odd or
even number of times, corresponding to the double connectedness of the SO(3)
group. An odd number of breaks leads to an additional $\pi$ phase to the
entangled state, but an even number of breaks does not. A scheme to trace the
evolution of the entangled state is proposed by means of entangled photon pairs
and Kerr medium, allowing observation of the additional $\pi$ phase.Comment: 4 pages, 3 figure

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### Communicability across evolving networks

Many natural and technological applications generate time ordered sequences of networks, deďŹned over a ďŹxed set of nodes; for example time-stamped information about âwho phoned whoâ or âwho came into contact with whoâ arise naturally in studies of communication and the spread of disease. Concepts and algorithms for static networks do not immediately carry through to this dynamic setting. For example, suppose A and B interact in the morning, and then B and C interact in the afternoon. Information, or disease, may then pass from A to C, but not vice versa. This subtlety is lost if we simply summarize using the daily aggregate network given by the chain A-B-C. However, using a natural deďŹnition of a walk on an evolving network, we show that classic centrality measures from the static setting can be extended in a computationally convenient manner. In particular, communicability indices can be computed to summarize the ability of each node to broadcast and receive information. The computations involve basic operations in linear algebra, and the asymmetry caused by timeâs arrow is captured naturally through the non-mutativity of matrix-matrix multiplication. Illustrative examples are given for both synthetic and real-world communication data sets. We also discuss the use of the new centrality measures for real-time monitoring and prediction

### Dynamic communicability predicts infectiousness

Using real, time-dependent social interaction data, we look at correlations between some recently proposed dynamic centrality measures and summaries from large-scale epidemic simulations. The evolving network arises from email exchanges. The centrality measures, which are relatively inexpensive to compute, assign rankings to individual nodes based on their ability to broadcast information over the dynamic topology. We compare these with node rankings based on infectiousness that arise when a full stochastic SI simulation is performed over the dynamic network. More precisely, we look at the proportion of the network that a node is able to infect over a fixed time period, and the length of time that it takes for a node to infect half the network.We find that the dynamic centrality measures are an excellent, and inexpensive, proxy for the full simulation-based measures

### Phase glass and zero-temperature phase transition in a randomly frustrated two-dimensional quantum rotor model

The ground state of the quantum rotor model in two dimensions with random
phase frustration is investigated. Extensive Monte Carlo simulations are
performed on the corresponding (2+1)-dimensional classical model under the
entropic sampling scheme. For weak quantum fluctuation, the system is found to
be in a phase glass phase characterized by a finite compressibility and a
finite value for the Edwards-Anderson order parameter, signifying long-ranged
phase rigidity in both spatial and imaginary time directions. Scaling
properties of the model near the transition to the gapped, Mott insulator state
with vanishing compressibility are analyzed. At the quantum critical point, the
dynamic exponent $z_{\rm dyn}\simeq 1.17$ is greater than one. Correlation
length exponents in the spatial and imaginary time directions are given by
$\nu\simeq 0.73$ and $\nu_z\simeq 0.85$, respectively, both assume values
greater than 0.6723 of the pure case. We speculate that the phase glass phase
is superconducting rather than metallic in the zero current limit.Comment: 14 pages, 4 figures, to appear in JSTA

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