A combinatorial smoothness criterion for spherical varieties

We suggest a combinatorial criterion for the smoothness of an arbitrary spherical variety using the classification of multiplicity-free spaces, generalizing an earlier result of Camus for spherical varieties of type $A$.Comment: 14 pages, 2 table

Quantum optical non-linearities induced by Rydberg-Rydberg interactions: a perturbative approach

In this article, we theoretically study the quantum statistical properties of the light transmitted through or reflected from an optical cavity, filled by an atomic medium with strong optical non-linearity induced by Rydberg-Rydberg van der Waals interactions. Atoms are driven on a two-photon transition from their ground state to a Rydberg level via an intermediate state by the combination of a weak signal field and a strong control beam. By using a perturbative approach, we get analytic results which remain valid in the regime of weak feeding fields, even when the intermediate state becomes resonant. Therefore they allow us to investigate quantitatively new features associated with the resonant behaviour of the system. We also propose an effective non-linear three-boson model of the system which, in addition to leading to the same analytic results as the original problem, sheds light on the physical processes at work in the system

Normality and smoothness of simple linear group compactifications

If G is a complex semisimple algebraic group, we characterize the normality and the smoothness of its simple linear compactifications, namely those equivariant GxG-compactifications which possess a unique closed orbit and which arise in a projective space of the shape P(End(V)), where V is finite dimensional rational G-module. Both the characterizations are purely combinatorial and are expressed in terms of the highest weights of V. In particular, we show that Sp(2r) (with r > 0) is the unique non-adjoint simple group which admits a simple smooth compactification.Comment: v2: minor changes, final version. To appear in Math.

Umbilical mechanism

Apparatus is described for automatically mating a pair of connectors and protecting them prior to mating, which minimizes weight and uses relatively simple and reliable mechanisms. Lower and upper connectors (24, 26) are held in lower and upper parts (14, 16) of a housing, with the upper connector mounted on a carrier (32) that is motor driven to move down and mate the connectors. A pair of movable members (36, 38) serve as shields, as coarse alignment aids, and as force transmitters. The movable members are pivotally mounted at the bottom of the upper housing, and as the carrier moves down it pivots the members out of the way. The movable members have socket elements (116) that closely receive pin elements (120) on the lower housing part, to coarsely align the connectors and to react mating and unmating forces between the housings. The carrier has a pair of plate portions (60, 62) with slots (64), and the movable members have cam followers engaged with the slot walls, to move the members with precision. The carrier plate-like portions engage follower members (82) that pivot open lower shield parts (44, 46) covering the lower connector, which is mounted on four stacks of Belleville washers (142)

Validity of adiabaticity in Cavity QED

This paper deals with the concept of adiabaticity for fully quantum mechanically cavity QED models. The physically interesting cases of Gaussian and standing wave shapes of the cavity mode are considered. An analytical approximate measure for adiabaticity is given and compared with numerical wave packet simulations. Good agreement is obtained where the approximations are expected to be valid. Usually for cavity QED systems, the large atom-field detuning case is considered as the adiabatic limit. We, however, show that adiabaticity is also valid, for the Gaussian mode shape, in the opposite limit. Effective semiclassical time dependent models, which do not take into account the shape of the wave packet, are derived. Corrections to such an effective theory, which are purely quantum mechanical, are discussed. It is shown that many of the results presented can be applied to time dependent two-level systems.Comment: 10 pages, 9 figure

Standard monomial theory for wonderful varieties

A general setting for a standard monomial theory on a multiset is introduced and applied to the Cox ring of a wonderful variety. This gives a degeneration result of the Cox ring to a multicone over a partial flag variety. Further, we deduce that the Cox ring has rational singularities.Comment: v3: 20 pages, final version to appear on Algebras and Representation Theory. The final publication is available at Springer via http://dx.doi.org/10.1007/s10468-015-9586-z. v2: 20 pages, examples added in Section 3 and in Section

A New X-Ray Flare from the Galactic Nucleus Detected with the XMM-Newton Photon Imaging Cameras

Sgr A*, the compact radio source, believed to be the counterpart of the massive black hole at the galactic nucleus, was observed to undergo rapid and intense flaring activity in X-rays with Chandra in October 2000. We report here the detection with XMM-Newton EPIC cameras of the early phase of a similar X-ray flare from this source, which occurred on September 4, 2001. The source 2-10 keV luminosity increased by a factor about 20 to reach a level of 4 10^{34} erg s^{-1} in a time interval of about 900 s, just before the end of the observation. The data indicate that the source spectrum was hard during the flare. This XMM-Newton observation confirms the results obtained by Chandra and suggests that, in Sgr A*, rapid and intense X-ray flaring is not a rare event. This can constrain the emission mechanism models proposed for this source, and also implies that the crucial multiwavelength observation programs planned to explore the behaviour of the radio/sub-mm and hard X-ray/gamma-ray emissions during the X-ray flares, have a good chance of success.Comment: 18 pages, 6 color figures, final version, accepted on October 24, 2002, to appear in ApJ, v584 n2 ApJ February 20, 2003 issu