Hierarchical analysis of gravitational-wave measurements of binary black hole spin-orbit misalignments

Binary black holes may form both through isolated binary evolution and through dynamical interactions in dense stellar environments. The formation channel leaves an imprint on the alignment between the black hole spins and the orbital angular momentum. Gravitational waves from these systems directly encode information about the spin--orbit misalignment angles, allowing them to be (weakly) constrained. Identifying sub-populations of spinning binary black holes will inform us about compact binary formation and evolution. We simulate a mixed population of binary black holes with spin--orbit misalignments modelled under a range of assumptions. We then develop a hierarchical analysis and apply it to mock gravitational-wave observations of these populations. Assuming a population with dimensionless spin magnitudes of $\chi = 0.7$, we show that tens of observations will make it possible to distinguish the presence of subpopulations of coalescing binary black holes based on their spin orientations. With $100$ observations it will be possible to infer the relative fraction of coalescing binary black holes with isotropic spin directions (corresponding to dynamical formation in our models) with a fractional uncertainty of $\sim 40\%$. Meanwhile, only $\sim 5$ observations are sufficient to distinguish between extreme models---all binary black holes either having exactly aligned spins or isotropic spin directions.Comment: 12 pages, 9 figures. Updated to match version published in MNRAS as 10.1093/mnras/stx176

Distributed Reasoning in a Peer-to-Peer Setting: Application to the Semantic Web

In a peer-to-peer inference system, each peer can reason locally but can also solicit some of its acquaintances, which are peers sharing part of its vocabulary. In this paper, we consider peer-to-peer inference systems in which the local theory of each peer is a set of propositional clauses defined upon a local vocabulary. An important characteristic of peer-to-peer inference systems is that the global theory (the union of all peer theories) is not known (as opposed to partition-based reasoning systems). The main contribution of this paper is to provide the first consequence finding algorithm in a peer-to-peer setting: DeCA. It is anytime and computes consequences gradually from the solicited peer to peers that are more and more distant. We exhibit a sufficient condition on the acquaintance graph of the peer-to-peer inference system for guaranteeing the completeness of this algorithm. Another important contribution is to apply this general distributed reasoning setting to the setting of the Semantic Web through the Somewhere semantic peer-to-peer data management system. The last contribution of this paper is to provide an experimental analysis of the scalability of the peer-to-peer infrastructure that we propose, on large networks of 1000 peers

Electronic spin precession and interferometry from spin-orbital entanglement in a double quantum dot

A double quantum dot inserted in parallel between two metallic leads allows to entangle the electron spin with the orbital (dot index) degree of freedom. An Aharonov-Bohm orbital phase can then be transferred to the spinor wavefunction, providing a geometrical control of the spin precession around a fixed magnetic field. A fully coherent behaviour is obtained in a mixed orbital/spin Kondo regime. Evidence for the spin precession can be obtained, either using spin-polarized metallic leads or by placing the double dot in one branch of a metallic loop.Comment: Final versio

An effective Hamiltonian for phase fluctuations on a lattice: an extended XY model

We derive an effective Hamiltonian for phase fluctuations in an s-wave superconductor starting from the attractive Hubbard model on a square lattice. In contrast to the common assumption, we find that the effective Hamiltonian is not the usual XY model but is of an extended XY type. This extended feature is robust and leads to essential corrections in understanding phase fluctuations on a lattice. The effective coupling in the Hamiltonian varies significantly with temperature.Comment: 2 figure

On the structure of spectra of travelling waves

The linear stability of the travelling wave solutions of a general reaction-diffusion system is investigated. The spectrum of the corresponding second order differential operator $L$ is studied. The problem is reduced to an asymptotically autonomous first order linear system. The relation between the spectrum of $L$ and the corresponding first order system is dealt with in detail. The first order system is investigated using exponential dichotomies. A self-contained short presentation is shown for the study of the spectrum, with elementary proofs. An algorithm is given for the determination of the exact position of the essential spectrum. The Evans function method for determining the isolated eigenvalues of $L$ is also presented. The theory is illustrated by three examples: a single travelling wave equation, a three variable combustion model and the generalized KdV equation

Detection of 84-GHz class I methanol maser emission towards NGC 253

We have investigated the central region of NGC 253 for the presence of 84.5-GHz ($5_{-1}\rightarrow4_0$E) methanol emission using the Australia Telescope Compact Array. We present the second detection of 84.5-GHz class~I methanol maser emission outside the Milky Way. This maser emission is offset from dynamical centre of NGC 253, in a region with previously detected emission from class~I maser transitions (36.2-GHz $4_{-1}\rightarrow3_0$E and 44.1-GHz $7_{0}\rightarrow6_1$A$^{+}$ methanol lines) . The emission features a narrow linewidth ($\sim$12 km s$^{-1}$) with a luminosity approximately 5 orders of magnitude higher than typical Galactic sources. We determine an integrated line intensity ratio of $1.2\pm0.4$ between the 36.2 GHz and 84.5-GHz class I methanol maser emission, which is similar to the ratio observed towards Galactic sources. The three methanol maser transitions observed toward NGC 253 each show a different distribution, suggesting differing physical conditions between the maser sites and that observations of additional class~I methanol transitions will facilitate investigations of the maser pumping regime.Comment: Accepted into ApJL 12 October 2018. 10 pages, 3 Figures and 2 Table

Critical Behavior of Coupled q-state Potts Models under Weak Disorder

We investigate the effect of weak disorder on different coupled $q$-state Potts models with $q\le 4$ using two loops renormalisation group. This study presents new examples of first order transitions driven by randomness. We found that weak disorder makes the models decouple. Therefore, it appears that no relations emerge, at a perturbation level, between the disordered $q_1\times q_2$-state Potts model and the two disordered $q_1$, $q_2$-state Potts models ($q_1\ne q_2$), despite their central charges are similar according to recent numerical investigations. Nevertheless, when two $q$-state Potts models are considered ($q>2$), the system remains always driven in a strong coupling regime, violating apparently the Imry-Wortis argument.Comment: 7 pages + 1 PS figure (Latex

Detecting nonlocal Cooper pair entanglement by optical Bell inequality violation

Based on the Bardeen Cooper Schrieffer (BCS) theory of superconductivity, the coherent splitting of Cooper pairs from a superconductor to two spatially separated quantum dots has been predicted to generate nonlocal pairs of entangled electrons. In order to test this hypothesis, we propose a scheme to transfer the spin state of a split Cooper pair onto the polarization state of a pair of optical photons. We show that the produced photon pairs can be used to violate a Bell inequality, unambiguously demonstrating the entanglement of the split Cooper pairs.Comment: 11 pages, 9 figures, v3 with added reference