Quantum Phase Transitions in the Interacting Boson Model: Integrability, level repulsion and level crossing

We study the quantum phase transition mechanisms that arise in the Interacting Boson Model. We show that the second-order nature of the phase transition from U(5) to O(6) may be attributed to quantum integrability, whereas all the first-order phase transitions of the model are due to level repulsion with one singular point of level crossing. We propose a model Hamiltonian with a true first-order phase transition for finite systems due to level crossings.Comment: Accepted in PR

A search for water maser emission toward obscured post-AGB star and planetary nebula candidates

Water maser emission at 22 GHz is a useful probe to study the transition between the nearly spherical mass-loss in the AGB to a collimated one in the post-AGB phase. In their turn, collimated jets in the post-AGB phase could determine the shape of planetary nebulae (PNe) once photoionization starts. We intend to find new cases of post-AGB stars and PNe with water maser emission, including water fountains or water-maser-emitting PNe. We observed water maser emission in a sample of 133 objects, with a significant fraction being post-AGB and young PN candidate sources with strong obscuration. We detected this emission in 15 of them, of which seven are reported here for the first time. We identified three water fountain candidates: IRAS 17291-2147, with a total velocity spread of ~96 km/s in its water maser components and two sources (IRAS 17021-3109 and IRAS 17348-2906) that show water maser emission outside the velocity range covered by OH masers. We have also identified IRAS 17393-2727 as a possible new water-maser-emitting PN. The detection rate is higher in obscured objects (14%) than in those with optical counterparts (7%), consistent with previous results. Water maser emission seems to be common in objects that are bipolar in the near-IR (43% detection rate). The water maser spectra of water fountain candidates like IRAS 17291-2147 show significantly less maser components than others (e.g., IRAS 18113-2503). We speculate that most post-AGBs may show water maser emission with wide enough velocity spread (> 100 km/s) when observed with enough sensitivity and/or for long enough periods of time. Therefore, it may be necessary to single out a special group of "water fountains", probably defined by their high maser luminosities. We also suggest that the presence of both water and OH masers in a PN is a better tracer of its youth, rather than the presence of just one of these species.Comment: To be published in Astronomy & Astrophysics. 16 pages, 1 figure (spanning 5 pages). This version includes some minor language corrections and fixes some errors in Table

The type N Karlhede bound is sharp

We present a family of four-dimensional Lorentzian manifolds whose invariant classification requires the seventh covariant derivative of the curvature tensor. The spacetimes in questions are null radiation, type N solutions on an anti-de Sitter background. The large order of the bound is due to the fact that these spacetimes are properly $CH_2$, i.e., curvature homogeneous of order 2 but non-homogeneous. This means that tetrad components of $R, \nabla R, \nabla^{(2)}R$ are constant, and that essential coordinates first appear as components of $\nabla^{(3)}R$. Covariant derivatives of orders 4,5,6 yield one additional invariant each, and $\nabla^{(7)}R$ is needed for invariant classification. Thus, our class proves that the bound of 7 on the order of the covariant derivative, first established by Karlhede, is sharp. Our finding corrects an outstanding assertion that invariant classification of four-dimensional Lorentzian manifolds requires at most $\nabla^{(6)}R$.Comment: 7 pages, typos corrected, added citation and acknowledgemen

The future of past tense: a cultural and studies centre for Gondar

The town of Gondar, in Northern Ethiopia, has won the prestigious status of a classified UNESCO world heritage site, in 26 October 1979, mainly because in it stands the castle compound locally known as the Atsie Fasil Ghimb. This palace compound encapsulates much of the country’s political and religious history between the mid-seventeenth century and the mid-nineteenth century, when Gondar was the capital of the Christian kingdom of Abyssinia

Integrability of Lie systems and some of its applications in physics

The geometric theory of Lie systems will be used to establish integrability conditions for several systems of differential equations, in particular Riccati equations and Ermakov systems. Many different integrability criteria in the literature will be analyzed from this new perspective and some applications in physics will be given.Comment: 16 page