Two examples of non strictly convex large deviations

We present two examples of a large deviations principle where the rate function is not strictly convex. This is motivated by a model used in mathematical finance (the Heston model), and adds a new item to the zoology of non strictly convex large deviations. For one of these examples, we show that the rate function of the Cramer-type of large deviations coincides with that of the Freidlin-Wentzell when contraction principles are applied.Comment: 11 page

Local density of states in metal - topological superconductor hybrid systems

We study by means of the recursive Green's function technique the local density-of-states of (finite and semi-infinite) multi-band spin-orbit coupled semiconducting nanowires in proximity to an s-wave superconductor and attached to normal-metal electrodes. When the nanowire is coupled to a normal electrode, the zero-energy peak, corresponding to the Majorana state in the topological phase, broadens with increasing transmission between the wire and the leads, eventually disappearing for ideal interfaces. Interestingly, for a finite transmission a peak is present also in the normal electrode, even though it has a smaller amplitude and broadens more rapidly with the strength of the coupling. Unpaired Majorana states can survive close to a topological phase transition even when the number of open channels (defined in the absence of superconductivity) is even. We finally study the Andreev-bound-state spectrum in superconductor-normal metal-superconductor junctions and find that in multi-band nanowires the distinction between topologically trivial and non-trivial systems based on the number of zero-energy crossings is preserved.Comment: 11 pages, 12 figures, published versio

Dark Monopoles in Grand Unified Theories

We consider a Yang-Mills-Higgs theory with gauge group $G=SU(n)$ broken to $G_{v} = [SU(p)\times SU(n-p)\times U(1)]/Z$ by a Higgs field in the adjoint representation. We obtain monopole solutions whose magnetic field is not in the Cartan Subalgebra. Since their magnetic field vanishes in the direction of the generator of the electromagnetic group $U(1)_{em}$, we call them Dark Monopoles. These Dark Monopoles must exist in some Grand Unified Theories (GUTs) without the need to introduce a dark sector. We analyze the particular case of $SU(5)$ GUT, where we obtain that their mass is $M = 4\pi v \widetilde{E}(\lambda/e^{2})/e$, where $\widetilde{E}(\lambda/e^{2})$ is a monotonically increasing function of $\lambda/e^{2}$ with $\widetilde{E}(0)=1.294$ and $\widetilde{E}(\infty)=3.262.$ We also give a geometrical interpretation to their non-abelian magnetic charge.Comment: 22 pages; added some comments on possible cosmological implications of Dark Monopoles in the last section and added some references. Published Versio

SwSt 1: an O-rich planetary nebula around a C-rich central star

The hydrogen-deficient carbon-rich [WCL] type central star HD167362 and its oxygen-rich planetary nebula (PN) SwSt~1 are investigated. The nebular chemistry might indicate a recent origin for the carbon-rich stellar spectrum. Its stellar and nebular properties might therefore provide further understanding of the origin of the [WCL] central star class. The UV-IR stellar spectra are modelled with state of the codes and show ~40kK central star with a wind and a C/O~3, indicative of efficient third dredge-up. The synthetic stellar flux distribution is used to model the high density, compact PN, which has a solar C/O ratio, is still enshrouded by 1200K and 230K dust shells and, reported here for the first time, in molecular hydrogen. Although it appears that the change in C/O ratio has been recent, the published spectroscopy since 1895 has been re-examined and no clear spectral change is seen. If an event occurred that has turned it into a hydrogen-deficient central star, it did not happen in the last 100 years.Comment: 31 pages, 19 figures (some are gif files), MNRAS in pres

Wolf-Rayet nebulae as tracers of stellar ionizing fluxes: I. M1-67

We use WR124 (WN8h) and its associated nebula M1-67, to test theoretical non-LTE models for Wolf-Rayet (WR) stars. Lyman continuum ionizing flux distributions derived from a stellar analysis of WR124, are compared with nebular properties via photo-ionization modelling. Our study demonstrates the significant role that line blanketing plays in affecting the Lyman ionizing energy distribution of WR stars, of particular relevance to the study of HII regions containing young stellar populations. We confirm previous results that non-line blanketed WR energy distributions fail to explain the observed nebular properties of M1-67, such that the predicted ionizing spectrum is too hard. A line blanketed analysis of WR124 is carried out using the method of Hillier & Miller (1998), with stellar properties in accord with previous results, except that the inclusion of clumping in the stellar wind reduces its wind performance factor to only approx2. The ionizing spectrum of the line blanketed model is much softer than for a comparable temperature unblanketed case, such that negligible flux is emitted with energy above the HeI 504 edge. Photo-ionization modelling, incorporating the observed radial density distribution for M1-67 reveals excellent agreement with the observed nebular electron temperature, ionization balance and line strengths. An alternative stellar model of WR124 is calculated, following the technique of de Koter et al. (1997), augmented to include line blanketing following Schmutz et al. (1991). Good consistency is reached regarding the stellar properties of WR124, but agreement with the nebular properties of M1-67 is somewhat poorer than for the Hillier & Miller code.Comment: 12 pages, 5 figures, latex2e style file, Astronomy & Astrophysics (accepted