Lectures on Linear Stability of Rotating Black Holes

These lecture notes are concerned with linear stability of the non-extreme Kerr geometry under perturbations of general spin. After a brief review of the Kerr black hole and its symmetries, we describe these symmetries by Killing fields and work out the connection to conservation laws. The Penrose process and superradiance effects are discussed. Decay results on the long-time behavior of Dirac waves are outlined. It is explained schematically how the Maxwell equations and the equations for linearized gravitational waves can be decoupled to obtain the Teukolsky equation. It is shown how the Teukolsky equation can be fully separated to a system of coupled ordinary differential equations. Linear stability of the non-extreme Kerr black hole is stated as a pointwise decay result for solutions of the Cauchy problem for the Teukolsky equation. The stability proof is outlined, with an emphasis on the underlying ideas and methods.Comment: 25 pages, LaTeX, 3 figures, lectures given at first DOMOSCHOOL in July 2018, minor improvements (published version

Relic densities including Sommerfeld enhancements in the MSSM

We have developed a general formalism to compute Sommerfeld enhancement (SE) factors for a multi-state system of fermions, in all possible spin configurations and with generic long-range interactions. We show how to include such SE effects in an accurate calculation of the thermal relic density for WIMP dark matter candidates. We apply the method to the MSSM and perform a numerical study of the relic abundance of neutralinos with arbitrary composition and including the SE due to the exchange of the W and Z bosons, photons and Higgses. We find that the relic density can be suppressed by a factor of a few in a seizable region of the parameter space, mostly for Wino-like neutralino with mass of a few TeV, and up to an order of magnitude close to a resonance.Comment: 23 pages, 7 figures; table 1 corrected and rearranged, numerical results practically unchanged, matches published versio

An exact expression to calculate the derivatives of position-dependent observables in molecular simulations with flexible constraints

In this work, we introduce an algorithm to compute the derivatives of physical observables along the constrained subspace when flexible constraints are imposed on the system (i.e., constraints in which the hard coordinates are fixed to configuration-dependent values). The presented scheme is exact, it does not contain any tunable parameter, and it only requires the calculation and inversion of a sub-block of the Hessian matrix of second derivatives of the function through which the constraints are defined. We also present a practical application to the case in which the sought observables are the Euclidean coordinates of complex molecular systems, and the function whose minimization defines the constraints is the potential energy. Finally, and in order to validate the method, which, as far as we are aware, is the first of its kind in the literature, we compare it to the natural and straightforward finite-differences approach in three molecules of biological relevance: methanol, N-methyl-acetamide and a tri-glycine peptideComment: 13 pages, 8 figures, published versio

Competition-based model of pheromone component ratio detection in the moth

For some moth species, especially those closely interrelated and sympatric, recognizing a specific pheromone component concentration ratio is essential for males to successfully locate conspecific females. We propose and determine the properties of a minimalist competition-based feed-forward neuronal model capable of detecting a certain ratio of pheromone components independently of overall concentration. This model represents an elementary recognition unit for the ratio of binary mixtures which we propose is entirely contained in the macroglomerular complex (MGC) of the male moth. A set of such units, along with projection neurons (PNs), can provide the input to higher brain centres. We found that (1) accuracy is mainly achieved by maintaining a certain ratio of connection strengths between olfactory receptor neurons (ORN) and local neurons (LN), much less by properties of the interconnections between the competing LNs proper. An exception to this rule is that it is beneficial if connections between generalist LNs (i.e. excited by either pheromone component) and specialist LNs (i.e. excited by one component only) have the same strength as the reciprocal specialist to generalist connections. (2) successful ratio recognition is achieved using latency-to-first-spike in the LN populations which, in contrast to expectations with a population rate code, leads to a broadening of responses for higher overall concentrations consistent with experimental observations. (3) when longer durations of the competition between LNs were observed it did not lead to higher recognition accuracy

Photonic quantum technologies

The first quantum technology, which harnesses uniquely quantum mechanical effects for its core operation, has arrived in the form of commercially available quantum key distribution systems that achieve enhanced security by encoding information in photons such that information gained by an eavesdropper can be detected. Anticipated future quantum technologies include large-scale secure networks, enhanced measurement and lithography, and quantum information processors, promising exponentially greater computation power for particular tasks. Photonics is destined for a central role in such technologies owing to the need for high-speed transmission and the outstanding low-noise properties of photons. These technologies may use single photons or quantum states of bright laser beams, or both, and will undoubtably apply and drive state-of-the-art developments in photonics

“It’s just a theory”: trainee science teachers’ misunderstandings of key scientific terminology

Background: This article presents the findings from a survey of 189 pre-service science teachers who were asked to provide definitions of key scientific terms ('theory'; 'fact'; 'law'; 'hypothesis'). The survey was a scoping and mapping exercise to establish the range and variety of definitions. Methods: Graduates on a pre-service science teacher training course were asked to complete a short, free response survey and define key science terminology a >95% response rate was achieved and respondents definitions were categorised according to a best fit model. Results: In some cases, definitions contrary to accepted scientific meanings were given. In other cases, terminology was defined in a wholly non-scientific way, e.g., one-fifth of the respondents defined a ‘law’ in the context of rules that govern society rather than in a scientific context. Science graduates’ definitions and their understanding of key terminology is poor despite their study of science in formal university settings (with many respondents being recent science graduates). Conclusions: Key terminology in science, such as 'theory', 'law', 'fact', 'hypothesis', tends not to be taught and defined with consideration for the differences in meaning that different audiences/users give to them. This article calls for better instruction for pre-service science teachers’ in the importance of accurate and precise definitions of key science terminology in order to better differentiate between the scientific and colloquial usage of key terms

Non-local effects in the mean-field disc dynamo. II. Numerical and asymptotic solutions

The thin-disc global asymptotics are discussed for axisymmetric mean-field dynamos with vacuum boundary conditions allowing for non-local terms arising from a finite radial component of the mean magnetic field at the disc surface. This leads to an integro-differential operator in the equation for the radial distribution of the mean magnetic field strength, $Q(r)$ in the disc plane at a distance $r$ from its centre; an asymptotic form of its solution at large distances from the dynamo active region is obtained. Numerical solutions of the integro-differential equation confirm that the non-local effects act similarly to an enhanced magnetic diffusion. This leads to a wider radial distribution of the eigensolution and faster propagation of magnetic fronts, compared to solutions with the radial surface field neglected. Another result of non-local effects is a slowly decaying algebraic tail of the eigenfunctions outside the dynamo active region, $Q(r)\sim r^{-4}$, which is shown to persist in nonlinear solutions where $\alpha$-quenching is included. The non-local nature of the solutions can affect the radial profile of the regular magnetic field in spiral galaxies and accretion discs at large distances from the centre.Comment: Revised version, as accepted; Geophys. Astrophys. Fluid Dyna

Quantum Computing

Quantum mechanics---the theory describing the fundamental workings of nature---is famously counterintuitive: it predicts that a particle can be in two places at the same time, and that two remote particles can be inextricably and instantaneously linked. These predictions have been the topic of intense metaphysical debate ever since the theory's inception early last century. However, supreme predictive power combined with direct experimental observation of some of these unusual phenomena leave little doubt as to its fundamental correctness. In fact, without quantum mechanics we could not explain the workings of a laser, nor indeed how a fridge magnet operates. Over the last several decades quantum information science has emerged to seek answers to the question: can we gain some advantage by storing, transmitting and processing information encoded in systems that exhibit these unique quantum properties? Today it is understood that the answer is yes. Many research groups around the world are working towards one of the most ambitious goals humankind has ever embarked upon: a quantum computer that promises to exponentially improve computational power for particular tasks. A number of physical systems, spanning much of modern physics, are being developed for this task---ranging from single particles of light to superconducting circuits---and it is not yet clear which, if any, will ultimately prove successful. Here we describe the latest developments for each of the leading approaches and explain what the major challenges are for the future.Comment: 26 pages, 7 figures, 291 references. Early draft of Nature 464, 45-53 (4 March 2010). Published version is more up-to-date and has several corrections, but is half the length with far fewer reference

Phase-locked indistinguishable photons with synthesized waveforms from a solid-state source

Resonance fluorescence in the Heitler regime provides access to single photons with coherence well beyond the Fourier transform limit of the transition, and holds the promise to circumvent environment-induced dephasing common to all solid-state systems. Here we demonstrate that the coherently generated single photons from a single self-assembled InAs quantum dot display mutual coherence with the excitation laser on a timescale exceeding 3 seconds. Exploiting this degree of mutual coherence we synthesize near-arbitrary coherent photon waveforms by shaping the excitation laser field. In contrast to post-emission filtering, our technique avoids both photon loss and degradation of the single photon nature for all synthesized waveforms. By engineering pulsed waveforms of single photons, we further demonstrate that separate photons generated coherently by the same laser field are fundamentally indistinguishable, lending themselves to creation of distant entanglement through quantum interference.Comment: Additional data and analysis in PDF format is available for download at the publications section of our website: http://www.amop.phy.cam.ac.uk/amop-ma

Framework, principles and recommendations for utilising participatory methodologies in the co-creation and evaluation of public health interventions

Background: Due to the chronic disease burden on society, there is a need for preventive public health interventions to stimulate society towards a healthier lifestyle. To deal with the complex variability between individual lifestyles and settings, collaborating with end-users to develop interventions tailored to their unique circumstances has been suggested as a potential way to improve effectiveness and adherence. Co-creation of public health interventions using participatory methodologies has shown promise but lacks a framework to make this process systematic. The aim of this paper was to identify and set key principles and recommendations for systematically applying participatory methodologies to co-create and evaluate public health interventions. Methods: These principles and recommendations were derived using an iterative reflection process, combining key learning from published literature in addition to critical reflection on three case studies conducted by research groups in three European institutions, all of whom have expertise in co-creating public health interventions using different participatory methodologies. Results: Key principles and recommendations for using participatory methodologies in public health intervention co-creation are presented for the stages of: Planning (framing the aim of the study and identifying the appropriate sampling strategy); Conducting (defining the procedure, in addition to manifesting ownership); Evaluating (the process and the effectiveness) and Reporting (providing guidelines to report the findings). Three scaling models are proposed to demonstrate how to scale locally developed interventions to a population level. Conclusions: These recommendations aim to facilitate public health intervention co-creation and evaluation utilising participatory methodologies by ensuring the process is systematic and reproducible