Causal geometries and third-order ordinary differential equations

We discuss contact invariant structures on the space of solutions of a third-order ordinary differential equation. Associated to any third-order differential equation modulo contact transformations, Chern introduced a degenerate conformal Lorentzian metric on the space of 2-jets of functions of one variable. When the Wuenschmann invariant vanishes, the degenerate metric descends to a proper conformal Lorentzian metric on the space of solutions. In the general case, when the Wuenschmann invariant is not zero, we define the notion of a causal geometry, and show that the space of solutions supports one. The Wuenschmann invariant is then related to the projective curvature of the indicatrix curve cut out by the causal geometry in the projective tangent space. When the Wuenschmann vanishes, the causal structure is then precisely the sheaf of null geodesics of the Chern conformal structure. We then introduce a Lagrangian and associated Hamiltonian from which the degenerate conformal Lorentzian metric are constructed. Finally, necessary and sufficient conditions are given for a rank three degenerate conformal Lorentzian metric in four dimensions to correspond to a third-order differential equation

Three-Algebras in N = 5, 6 Superconformal Chern-Simons Theories: Representations and Relations

In this work we present 3-algebraic constructions and representations for three-dimensional N = 5 supersymmetric Chern-Simons theories, and show how they relate to theories with additional supersymmetries. The N = 5 structure constants give theories with Sp(2N) \times SO(M) gauge symmetry, as well as more exotic symmetries known from gauged supergravity. We find explicit lifts from N = 6 to 8, and N = 5 to 6 and 8, for appropriate gauge groups.Comment: 23 pages. Published version. References correcte

What is the scope to test a smoking cessation intervention aimed at young people admitted to hospital?

Background: Young adults are reluctant to use evidence-based smoking cessation interventions. Subsequently, they are less successful at giving up smoking compared to older adults. This highlights the need for innovative strategies to engage young people in smoking cessation. A novel intervention using photoageing technology has been shown to be an effective trigger for smoking cessation. Aims: To conduct a pilot study deploying photoageing care technology to trigger smoking cessation attempts in young adults admitted to hospital. Method: A randomised controlled trial was designed. Thirty participants were recruited from a regional hospital in Melbourne, Australia. Participants were allocated to the intervention and control groups on alternate weeks. All participants received brief smoking cessation advice. The intervention group was digitally aged using the APRIL Face Aging Software. The primary outcomes were measured at six weeks’ post-intervention and included number of quit attempts, nicotine dependence, and progression through the stages of change model. Results: At six weeks’ post-intervention, there was no difference in quit attempts between the two groups (Mann-Whitney U=111 and p=0.484). There was also no difference in nicotine dependence (Mann-Whitney U=106 and p=0.403) or stage of change (2=1.71 and p=0.634) between the groups. Conclusion: Hospitalisation is associated with a number of barriers, which prevent the implementation of photoageing technology in this setting. Of these barriers, participant recruitment and retention pose the greatest challenge. Due to these considerations, it was not possible to demonstrate an effect size with any confidence

Thermalization and breakdown of thermalization in photon condensates

The authors acknowledge financial support from EPSRC program “TOPNES” (Grant No. EP/I031014/1) and EPSRC (Grant No. EP/G004714/2). P.G.K. acknowledges support from EPSRC (Grant No. EP/M010910/1).We examine in detail the mechanisms behind thermalization and Bose-Einstein condensation (BEC) of a gas of photons in a dye-filled microcavity. We derive a microscopic quantum model, based on that of a standard laser, and show how this model can reproduce the behavior of recent experiments. Using the rate-equation approximation of this model, we show how a thermal distribution of photons arises. We go on to describe how the nonequilibrium effects in our model can cause thermalization to break down as one moves away from the experimental parameter values. In particular, we examine the effects of changing cavity length, and of altering the vibrational spectrum of the dye molecules. We are able to identify two measures which quantify whether the system is in thermal equilibrium. Using these, we plot “phase diagrams” distinguishing BEC and standard lasing regimes. Going beyond the rate-equation approximation, our quantum model allows us to investigate both the second-order coherence g(2) and the linewidth of the emission from the cavity. We show how the linewidth collapses as the system transitions to a Bose condensed state, and compare the results to the Schawlow-Townes linewidth.Publisher PDFPeer reviewe