A "Baedecker" for the Dark Matter Annihilation Signal

We provide a ``Baedecker'' or travel guide to the directions on the sky where the dark matter annihilation signal may be expected. We calculate the flux of high energy gamma-rays from annihilation of neutralino dark matter in the centre of the Milky Way and the three nearest dwarf spheroidals (Sagittarius, Draco and Canis Major), using realistic models of the dark matter distribution. Other investigators have used cusped dark halo profiles (such as the Navarro-Frenk-White) to claim a significant signal. This ignores the substantial astrophysical evidence that the Milky Way is not dark-matter dominated in the inner regions. We show that the annihilation signal from the Galactic Centre falls by two orders of magnitude on substituting a cored dark matter density profile for a cusped one. The present and future generation of high energy gamma-ray detectors, whether atmospheric Cerenkov telescopes or space missions like GLAST, lack the sensitivity to detect any of the monochromatic gamma-ray annihilation lines. The continuum gamma-ray signal above 1 GeV and above 50 GeV may however be detectable either from the dwarf spheroidals or from the Milky Way itself. If the density profiles of the dwarf spheroidals are cusped, then the best prospects are for detecting Sagittarius and Canis Major. However, if the dwarf spheroidals have milder, cored profiles, then the annihilation signal is not detectable. For GLAST, an attractive strategy is to exploit the wide field of view and observe the Milky Way at medium latitudes, as suggested by Stoehr et al. This is reasonably robust against changes in the density profile.Comment: 13 pages, 3 figures, version in press at The Physical Review

Floquet analysis of pulsed Dirac systems: A way to simulate rippled graphene

The low energy continuum limit of graphene is effectively known to be modeled using Dirac equation in (2+1) dimensions. We consider the possibility of using modulated high frequency periodic driving of a two-dimension system (optical lattice) to simulate properties of rippled graphene. We suggest that the Dirac Hamiltonian in a curved background space can also be effectively simulated by a suitable driving scheme in optical lattice. The time dependent system yields, in the approximate limit of high frequency pulsing, an effective time independent Hamiltonian that governs the time evolution, except for an initial and a final kick. We use a specific form of 4-phase pulsed forcing with suitably tuned choice of modulating operators to mimic the effects of curvature. The extent of curvature is found to be directly related to $\omega^{-1}$ the time period of the driving field at the leading order. We apply the method to engineer the effects of curved background space. We find that the imprint of curvilinear geometry modifies the electronic properties, such as LDOS, significantly. We suggest that this method shall be useful in studying the response of various properties of such systems to non-trivial geometry without requiring any actual physical deformations.Comment: 16 pages, 1 figure. Suggestions and comments are welcom

Consensus in the Presence of Multiple Opinion Leaders: Effect of Bounded Confidence

The problem of analyzing the performance of networked agents exchanging evidence in a dynamic network has recently grown in importance. This problem has relevance in signal and data fusion network applications and in studying opinion and consensus dynamics in social networks. Due to its capability of handling a wider variety of uncertainties and ambiguities associated with evidence, we use the framework of Dempster-Shafer (DS) theory to capture the opinion of an agent. We then examine the consensus among agents in dynamic networks in which an agent can utilize either a cautious or receptive updating strategy. In particular, we examine the case of bounded confidence updating where an agent exchanges its opinion only with neighboring nodes possessing 'similar' evidence. In a fusion network, this captures the case in which nodes only update their state based on evidence consistent with the node's own evidence. In opinion dynamics, this captures the notions of Social Judgment Theory (SJT) in which agents update their opinions only with other agents possessing opinions closer to their own. Focusing on the two special DS theoretic cases where an agent state is modeled as a Dirichlet body of evidence and a probability mass function (p.m.f.), we utilize results from matrix theory, graph theory, and networks to prove the existence of consensus agent states in several time-varying network cases of interest. For example, we show the existence of a consensus in which a subset of network nodes achieves a consensus that is adopted by follower network nodes. Of particular interest is the case of multiple opinion leaders, where we show that the agents do not reach a consensus in general, but rather converge to 'opinion clusters'. Simulation results are provided to illustrate the main results.Comment: IEEE Transactions on Signal and Information Processing Over Networks, to appea