Spectrum of the Vortex Bound States of the Dirac and Schrodinger Hamiltonian in the presence of Superconducting Gaps

We investigate the vortex bound states both Schrodinger and Dirac Hamiltonian with the s-wave superconducting pairing gap by solving the mean-field Bogoliubov-de-Gennes equations. The exact vortex bound states spectrum is numerically determined by the integration method, and also accompanied by the quasi-classical analysis. It is found that the bound state energies is proportional to the vortex angular momentum when the chemical potential is large enough. By applying the external magnetic field, the vortex bound state energies of the Dirac Hamiltonian are almost unchanged; whereas the energy shift of the Schrodinger Hamiltonian is proportional to the magnetic field. These qualitative differences may serve as an indirect evidence of the existence of Majorana fermions in which the zero mode exists in the case of the Dirac Hamiltonian only.Comment: 8 pages, 9 figure

Jet disc coupling in black hole binaries

In the last decade multi-wavelength observations have demonstrated the importance of jets in the energy output of accreting black hole binaries. The observed correlations between the presence of a jet and the state of the accretion flow provide important information on the coupling between accretion and ejection processes. After a brief review of the properties of black hole binaries, I illustrate the connection between accretion and ejection through two particularly interesting examples. First, an INTEGRAL observation of Cygnus X-1 during a 'mini-' state transition reveals disc jet coupling on time scales of orders of hours. Second, the black hole XTEJ1118+480 shows complex correlations between the X-ray and optical emission. Those correlations are interpreted in terms of coupling between disc and jet on time scales of seconds or less. Those observations are discussed in the framework of current models.Comment: Invited talk at the Fifth Stromlo Symposium: Disks, Winds & Jets - from Planets to Quasars. Accepted for publication in Astrophysics & Space Scienc

A fast single server private information retrieval protocol with low communication cost

Existing single server Private Information Retrieval (PIR) protocols are far from practical. To be practical, a single server PIR protocol has to be both communicationally and computationally efficient. In this paper, we present a single server PIR protocol that has low communication cost and is much faster than existing protocols. A major building block of the PIR protocol in this paper is a tree-based compression scheme, which we call folding/unfolding. This compression scheme enables us to lower the communication complexity to O(loglogn). The other major building block is the BGV fully homomorphic encryption scheme. We show how we design the protocol to exploit the internal parallelism of the BGV scheme. This significantly reduces the server side computational overhead and makes our protocol much faster than the existing protocols. Our protocol can be further accelerated by utilising hardware parallelism. We have built a prototype of the protocol. We report on the performance of our protocol based on the prototype and compare it with the current most efficient protocols

Semiclassical theory of transport in a random magnetic field

We study the semiclassical kinetics of 2D fermions in a smoothly varying magnetic field $B({\bf r})$. The nature of the transport depends crucially on both the strength $B_0$ of the random component of $B({\bf r})$ and its mean value $\bar{B}$. For $\bar{B}=0$, the governing parameter is $\alpha=d/R_0$, where $d$ is the correlation length of disorder and $R_0$ is the Larmor radius in the field $B_0$. While for $\alpha\ll 1$ the Drude theory applies, at $\alpha\gg 1$ most particles drift adiabatically along closed contours and are localized in the adiabatic approximation. The conductivity is then determined by a special class of trajectories, the "snake states", which percolate by scattering at the saddle points of $B({\bf r})$ where the adiabaticity of their motion breaks down. The external field also suppresses the diffusion by creating a percolation network of drifting cyclotron orbits. This kind of percolation is due only to a weak violation of the adiabaticity of the cyclotron rotation, yielding an exponential drop of the conductivity at large $\bar{B}$. In the regime $\alpha\gg 1$ the crossover between the snake-state percolation and the percolation of the drift orbits with increasing $\bar{B}$ has the character of a phase transition (localization of snake states) smeared exponentially weakly by non-adiabatic effects. The ac conductivity also reflects the dynamical properties of particles moving on the fractal percolation network. In particular, it has a sharp kink at zero frequency and falls off exponentially at higher frequencies. We also discuss the nature of the quantum magnetooscillations. Detailed numerical studies confirm the analytical findings. The shape of the magnetoresistivity at $\alpha\sim 1$ is in good agreement with experimental data in the FQHE regime near $\nu=1/2$.Comment: 22 pages REVTEX, 14 figure

Lattice Pseudospin Model for ν=1\nu=1 Quantum Hall Bilayers

We present a new theoretical approach to the study of $\nu=1$ quantum Hall bilayer that is based on a systematic mapping of the microscopic Hamiltonian to an anisotropic SU(4) spin model on a lattice. To study the properties of this model we generalize the Heisenberg model Schwinger boson mean field theory (SBMFT) of Arovas and Auerbach to spin models with anisotropy. We calculate the temperature dependence of experimentally observable quantities, including the spin magnetization, and the differential interlayer capacitance. Our theory represents a substantial improvement over the conventional Hartree-Fock picture which neglects quantum and thermal fluctuations, and has advantages over long-wavelength effective models that fail to capture important microscopic physics at all realistic layer separations. The formalism we develop can be generalized to treat quantum Hall bilayers at filling factor $\nu=2$.Comment: 26 pages, 10 figures. The final version, to appear in PR

Modelling spectral and timing properties of accreting black holes: the hybrid hot flow paradigm

The general picture that emerged by the end of 1990s from a large set of optical and X-ray, spectral and timing data was that the X-rays are produced in the innermost hot part of the accretion flow, while the optical/infrared (OIR) emission is mainly produced by the irradiated outer thin accretion disc. Recent multiwavelength observations of Galactic black hole transients show that the situation is not so simple. Fast variability in the OIR band, OIR excesses above the thermal emission and a complicated interplay between the X-ray and the OIR light curves imply that the OIR emitting region is much more compact. One of the popular hypotheses is that the jet contributes to the OIR emission and even is responsible for the bulk of the X-rays. However, this scenario is largely ad hoc and is in contradiction with many previously established facts. Alternatively, the hot accretion flow, known to be consistent with the X-ray spectral and timing data, is also a viable candidate to produce the OIR radiation. The hot-flow scenario naturally explains the power-law like OIR spectra, fast OIR variability and its complex relation to the X-rays if the hot flow contains non-thermal electrons (even in energetically negligible quantities), which are required by the presence of the MeV tail in Cyg X-1. The presence of non-thermal electrons also lowers the equilibrium electron temperature in the hot flow model to <100 keV, making it more consistent with observations. Here we argue that any viable model should simultaneously explain a large set of spectral and timing data and show that the hybrid (thermal/non-thermal) hot flow model satisfies most of the constraints.Comment: 26 pages, 13 figures. To be published in the Space Science Reviews and as hard cover in the Space Sciences Series of ISSI - The Physics of Accretion on to Black Holes (Springer Publisher

Variational and Geometric Structures of Discrete Dirac Mechanics

In this paper, we develop the theoretical foundations of discrete Dirac mechanics, that is, discrete mechanics of degenerate Lagrangian/Hamiltonian systems with constraints. We first construct discrete analogues of Tulczyjew's triple and induced Dirac structures by considering the geometry of symplectic maps and their associated generating functions. We demonstrate that this framework provides a means of deriving discrete Lagrange-Dirac and nonholonomic Hamiltonian systems. In particular, this yields nonholonomic Lagrangian and Hamiltonian integrators. We also introduce discrete Lagrange-d'Alembert-Pontryagin and Hamilton-d'Alembert variational principles, which provide an alternative derivation of the same set of integration algorithms. The paper provides a unified treatment of discrete Lagrangian and Hamiltonian mechanics in the more general setting of discrete Dirac mechanics, as well as a generalization of symplectic and Poisson integrators to the broader category of Dirac integrators.Comment: 26 pages; published online in Foundations of Computational Mathematics (2011

Mystify me: Coke, terror and the symbolic immortality boost

A panel on “Marketing as Mystification” convened at the 2011 Academy of Marketing conference in Liverpool. Ideas from the Liverpool event were supplemented by commentaries from selected other authors. Each commentary explores the aspects of “mystification” observable in marketing discourses and practices. In what follows, Laufer interprets marketing mystification as modern form of sophism, Dholakia and Firat discuss mystifying ways that inequality is marketed, Varman analyzes the perversion and mystification of “development” via neoliberal marketing of “social entrepreneurship,” Mikkonen explores mystifying marketing representations of gays and lesbians, and Freund and Jacobi present a fascinating interpretation of how Coca-Cola advertising mystically reassures us that our difficult, dangerous lifeworld is actually quite hunky-dory. </jats:p

Planck 2015 results. XXVII. The Second Planck Catalogue of Sunyaev-Zeldovich Sources

We present the all-sky Planck catalogue of Sunyaev-Zeldovich (SZ) sources detected from the 29 month full-mission data. The catalogue (PSZ2) is the largest SZ-selected sample of galaxy clusters yet produced and the deepest all-sky catalogue of galaxy clusters. It contains 1653 detections, of which 1203 are confirmed clusters with identified counterparts in external data-sets, and is the first SZ-selected cluster survey containing > $10^3$ confirmed clusters. We present a detailed analysis of the survey selection function in terms of its completeness and statistical reliability, placing a lower limit of 83% on the purity. Using simulations, we find that the Y5R500 estimates are robust to pressure-profile variation and beam systematics, but accurate conversion to Y500 requires. the use of prior information on the cluster extent. We describe the multi-wavelength search for counterparts in ancillary data, which makes use of radio, microwave, infra-red, optical and X-ray data-sets, and which places emphasis on the robustness of the counterpart match. We discuss the physical properties of the new sample and identify a population of low-redshift X-ray under- luminous clusters revealed by SZ selection. These objects appear in optical and SZ surveys with consistent properties for their mass, but are almost absent from ROSAT X-ray selected samples

The distribution of radioactive 44Ti in Cassiopeia A

The distribution of elements produced in the innermost layers of a supernova explosion is a key diagnostic for studying the collapse of massive stars. Here we present the results of a 2.4 Ms NuSTAR observing campaign aimed at studying the supernova remnant Cassiopeia A (Cas A). We perform spatially resolved spectroscopic analyses of the 44Ti ejecta, which we use to determine the Doppler shift and thus the three-dimensional (3D) velocities of the 44Ti ejecta. We find an initial 44Ti mass of (1.54 ± 0.21) × 10−4 M⊙, which has a present-day average momentum direction of 340° ± 15° projected onto the plane of the sky (measured clockwise from celestial north) and is tilted by 58° ± 20° into the plane of the sky away from the observer, roughly opposite to the inferred direction of motion of the central compact object. We find some 44Ti ejecta that are clearly interior to the reverse shock and some that are clearly exterior to it. Where we observe 44Ti ejecta exterior to the reverse shock we also see shock-heated iron; however, there are regions where we see iron but do not observe 44Ti. This suggests that the local conditions of the supernova shock during explosive nucleosynthesis varied enough to suppress the production of 44Ti by at least a factor of two in some regions, even in regions that are assumed to be the result of processes like α-rich freezeout that should produce both iron and titanium