Towards a Coulomb gas of instantons in the SO(4)xU(1) Higgs model on R_4

The $SO(4)\times U(1)$ Higgs model on $\R_4$ is extended by a $F^3$ term so that the action receives a nonvanishing contribution from the interactions of 2-instantons and 3-instantons, and can be expressed as the inverse of the Laplacian on $\R_4$ in terms of the mutual distances of the instantons. The one-instanton solutions of both the basic and the extended models have been studied in detail numerically.Comment: 29 pages LaTeX, 4 Figures available from authors on reques

Measuring a photonic qubit without destroying it

Measuring the polarisation of a single photon typically results in its destruction. We propose, demonstrate, and completely characterise a \emph{quantum non-demolition} (QND) scheme for realising such a measurement non-destructively. This scheme uses only linear optics and photo-detection of ancillary modes to induce a strong non-linearity at the single photon level, non-deterministically. We vary this QND measurement continuously into the weak regime, and use it to perform a non-destructive test of complementarity in quantum mechanics. Our scheme realises the most advanced general measurement of a qubit: it is non-destructive, can be made in any basis, and with arbitrary strength.Comment: 4 pages, 3 figure

Giant optical Faraday rotation induced by a single electron spin in a quantum dot: Applications to entangling remote spins via a single photon

We propose a quantum non-demolition method - giant Faraday rotation - to detect a single electron spin in a quantum dot inside a microcavity where negatively-charged exciton strongly couples to the cavity mode. Left- and right-circularly polarized light reflected from the cavity feels different phase shifts due to cavity quantum electrodynamics and the optical spin selection rule. This yields giant and tunable Faraday rotation which can be easily detected experimentally. Based on this spin-detection technique, a scalable scheme to create an arbitrary amount of entanglement between two or more remote spins via a single photon is proposed.Comment: 5 pages, 3 figure

Changing social contracts in climate-change adaptation

Risks from extreme weather events are mediated through state, civil society and individual action 1 , 2 . We propose evolving social contracts as a primary mechanism by which adaptation to climate change proceeds. We use a natural experiment of policy and social contexts of the UK and Ireland affected by the same meteorological event and resultant flooding in November 2009. We analyse data from policy documents and from household surveys of 356 residents in western Ireland and northwest England. We find significant differences between perceptions of individual responsibility for protection across the jurisdictions and between perceptions of future risk from populations directly affected by flooding events. These explain differences in stated willingness to take individual adaptive actions when state support retrenches. We therefore show that expectations for state protection are critical in mediating impacts and promoting longer-term adaptation. We argue that making social contracts explicit may smooth pathways to effective and legitimate adaptation

Finite energy/action solutions of p1p_1 Yang-Mills equations on p2p_2 Schwarzschild and deSitter backgrounds for dimension d≥4d \ge 4

Physically relevant gauge and gravitational theories can be seen as special members of hierarchies of more elaborate systems. The Yang-Mills (YM) system is the first member of a hierarchy of Lagrangians which we will index by $p_1$, and the Einstein-Hilbert (EH) system of general relativity is the first member of another hierarchy which we index by $p_2$. In this paper, we study the classical equations of the $p_1 = 1,2$ YM hierarchy considered in the background of special geometries (Schwarzschild, deSitter,anti-deSitter) of the $p_2=1,2,3$ EH hierarchy. Solutions are obtained in various dimensions and lead to several examples of non-self-dual YM fields. When $p_1=p_2$ self-dual solutions exist in addition. Their action is equal to the Chern-Pontryagin charge and can be compared with that of the non-self-dual solutions.Comment: LaTeX, 25 pages, 2 figures, new title, minor change

Measuring the Impact of Nextstep Career Advice in the North East of England

In September, 2007, the main contractors of the four nextstep networks in the North East (referred to in this paper as the ‘consortium’) successfully submitted a proposal to the Learning & Skills Council (LSC) for funding to develop a framework for measuring the impact of career advice. It was agreed that the project would result in a practice-based ‘Impact Toolkit’ that would include:- • a set of impact measures that should be used in the new adult careers service with a rationale for their inclusion; • methodologies for each of the impact measures identified; • approaches to obtaining information on progression in learning and work – with templates and case study material; • approaches to measuring soft outcomes; and • suggested Key Performance Indicators (KPIs)

Swift observations of the 2006 outburst of the recurrent nova RS Ophiuchi: I. Early X-ray emission from the shocked ejecta and red giant wind

RS Ophiuchi began its latest outburst on 2006 February 12. Previous outbursts have indicated that high velocity ejecta interact with a pre-existing red giant wind, setting up shock systems analogous to those seen in Supernova Remnants. However, in the previous outburst in 1985, X-ray observations did not commence until 55 days after the initial explosion. Here we report on Swift observations covering the first month of the 2006 outburst with the Burst Alert (BAT) and X-ray Telescope (XRT) instruments. RS Oph was clearly detected in the BAT 14-25 keV band from t=0 to $t\sim6$ days. XRT observationsfrom 0.3-10 keV, started at 3.17 days after outburst. The rapidly evolving XRT spectra clearly show the presence of both line and continuum emission which can be fitted by thermal emission from hot gas whose characteristic temperature, overlying absorbing column, $[N_H]_W$, and resulting unabsorbed total flux decline monotonically after the first few days. Derived shock velocities are in good agreement with those found from observations at other wavelengths. Similarly, $[N_H]_W$ is in accord with that expected from the red giant wind ahead of the forward shock. We confirm the basic models of the 1985 outburst and conclude that standard Phase I remnant evolution terminated by $t\sim10$ days and the remnant then rapidly evolved to display behaviour characteristic of Phase III. Around t=26 days however, a new, luminous and highly variable soft X-ray source began to appear whose origin will be explored in a subsequent paper.Comment: 20 pages, 4 figures (2 updated), accepted by Ap

Quantum Non-demolition Measurements on Qubits

We discuss the characterization and properties of quantum non-demolition (QND) measurements on qubit systems. We introduce figures of merit which can be applied to systems of any Hilbert space dimension thus providing universal criteria for characterizing QND measurements. We discuss the controlled-NOT gate and an optical implementation as examples of QND devices for qubits. We also discuss the QND measurement of weak values

Limitations of the Standard Gravitational Perfect Fluid Paradigm

We show that the standard perfect fluid paradigm is not necessarily a valid description of a curved space steady state gravitational source. Simply by virtue of not being flat, curved space geometries have to possess intrinsic length scales, and such length scales can affect the fluid structure. For modes of wavelength of order or greater than such scales eikonalized geometrical optics cannot apply and rays are not geodesic. Covariantizing thus entails not only the replacing of flat space functions by covariant ones, but also the introduction of intrinsic scales that were absent in flat space. In principle it is thus unreliable to construct the curved space energy-momentum tensor as the covariant generalization of a geodesic-based flat spacetime energy-momentum tensor. By constructing the partition function as an incoherent average over a complete set of modes of a scalar field propagating in a curved space background, we show that for the specific case of a static, spherically symmetric geometry, the steady state energy-momentum tensor that ensues will in general be of the form $T_{\mu\nu}=(\rho+p)U_{\mu}U_{\nu}+pg_{\mu\nu}+\pi_{\mu\nu}$ where the anisotropic $\pi_{\mu\nu}$ is a symmetric, traceless rank two tensor which obeys $U^{\mu}\pi_{\mu\nu}=0$. Such a $\pi_{\mu\nu}$ type term is absent for an incoherently averaged steady state fluid in a spacetime where there are no intrinsic length scales, and in principle would thus be missed in a covariantizing of a flat spacetime $T_{\mu\nu}$. While the significance of such $\pi_{\mu\nu}$ type terms would need to be evaluated on a case by case basis, through the use of kinetic theory we reassuringly find that the effect of such $\pi_{\mu\nu}$ type terms is small for weak gravity stars where perfect fluid sources are commonly used.Comment: Final version to appear in General Relativity and Gravitation (the final publication is available at http://www.springerlink.com). 29 pages, 1 figur

Testing the standard fireball model of GRBs using late X-ray afterglows measured by Swift

We show that all X-ray decay curves of GRBs measured by Swift can be fitted using one or two components both of which have exactly the same functional form comprised of an early falling exponential phase followed by a power law decay. The 1st component contains the prompt gamma-ray emission and the initial X-ray decay. The 2nd component appears later, has a much longer duration and is present for ~80% of GRBs. It most likely arises from the external shock which eventually develops into the X-ray afterglow. In the remaining ~20% of GRBs the initial X-ray decay of the 1st component fades more slowly than the 2nd and dominates at late times to form an afterglow but it is not clear what the origin of this emission is. The temporal decay parameters and gamma/X-ray spectral indices derived for 107 GRBs are compared to the expectations of the standard fireball model including a search for possible "jet breaks". For ~50% of GRBs the observed afterglow is in accord with the model but for the rest the temporal and spectral indices do not conform to the expected closure relations and are suggestive of continued, late, energy injection. We identify a few possible jet breaks but there are many examples where such breaks are predicted but are absent. The time, T_a, at which the exponential phase of the 2nd component changes to a final powerlaw decay afterglow is correlated with the peak of the gamma-ray spectrum, E_peak. This is analogous to the Ghirlanda relation, indicating that this time is in some way related to optically observed break times measured for pre-Swift bursts.Comment: submitted to Ap