On p-adic lattices and Grassmannians

It is well-known that the coset spaces G(k((z)))/G(k[[z]]), for a reductive group G over a field k, carry the geometric structure of an inductive limit of projective k-schemes. This k-ind-scheme is known as the affine Grassmannian for G. From the point of view of number theory it would be interesting to obtain an analogous geometric interpretation of quotients of the form G(W(k)[1/p])/G(W(k)), where p is a rational prime, W denotes the ring scheme of p-typical Witt vectors, k is a perfect field of characteristic p and G is a reductive group scheme over W(k). The present paper is an attempt to describe which constructions carry over from the function field case to the p-adic case, more precisely to the situation of the p-adic affine Grassmannian for the special linear group G=SL_n. We start with a description of the R-valued points of the p-adic affine Grassmannian for SL_n in terms of lattices over W(R), where R is a perfect k-algebra. In order to obtain a link with geometry we further construct projective k-subvarieties of the multigraded Hilbert scheme which map equivariantly to the p-adic affine Grassmannian. The images of these morphisms play the role of Schubert varieties in the p-adic setting. Further, for any reduced k-algebra R these morphisms induce bijective maps between the sets of R-valued points of the respective open orbits in the multigraded Hilbert scheme and the corresponding Schubert cells of the p-adic affine Grassmannian for SL_n.Comment: 36 pages. This is a thorough revision, in the form accepted by Math. Zeitschrift, of the previously published preprint "On p-adic loop groups and Grassmannians

Times of arrival: Bohm beats Kijowski

We prove that the Bohmian arrival time of the 1D Schroedinger evolution violates the quadratic form structure on which Kijowski's axiomatic treatment of arrival times is based. Within Kijowski's framework, for a free right moving wave packet, the various notions of arrival time (at a fixed point x on the real line) all yield the same average arrival time. We derive an inequality relating the average Bohmian arrival time to the one of Kijowksi. We prove that the average Bohmian arrival time is less than Kijowski's one if and only if the wave packet leads to position probability backflow through x. Otherwise the two average arrival times coincide.Comment: 9 page

A new approach to quantum backflow

We derive some rigorous results concerning the backflow operator introduced by Bracken and Melloy. We show that it is linear bounded, self adjoint, and not compact. Thus the question is underlined whether the backflow constant is an eigenvalue of the backflow operator. From the position representation of the backflow operator we obtain a more efficient method to determine the backflow constant. Finally, detailed position probability flow properties of a numerical approximation to the (perhaps improper) wave function of maximal backflow are displayed.Comment: 12 pages, 8 figure

Bohmian transmission and reflection dwell times without trajectory sampling

Within the framework of Bohmian mechanics dwell times find a straightforward formulation. The computation of associated probabilities and distributions however needs the explicit knowledge of a relevant sample of trajectories and therefore implies formidable numerical effort. Here a trajectory free formulation for the average transmission and reflection dwell times within static spatial intervals [a,b] is given for one-dimensional scattering problems. This formulation reduces the computation time to less than 5% of the computation time by means of trajectory sampling.Comment: 14 pages, 7 figures; v2: published version, significantly revised and shortened (former sections 2 and 3 omitted, appendix A added, simplified mathematics

Diffraction in time of a confined particle and its Bohmian paths

Diffraction in time of a particle confined in a box which its walls are removed suddenly at $t=0$ is studied. The solution of the time-dependent Schr\"{o}dinger equation is discussed analytically and numerically for various initial wavefunctions. In each case Bohmian trajectories of the particles are computed and also the mean arrival time at a given location is studied as a function of the initial state.Comment: 8 pages, 6 figure

Ethanol Vapours to Complement or Replace Sulfur Dioxide Fumigation of Table Grapes

Recent studies have shown that dipping table grapes in ethanol solutions at harvest improved storage of the fruit. We report here the first results obtained by treating "Chasselas" table grapes (Vitis vinifera) with ethanol vapours over the storage period. We tested the effect of ethanol at 0, 4 and 8 g/kg fruit during cold storage for 2, 4 and 6 weeks. We measured berry shatter, stem browning, Botrytis rot incidence and sensory appreciation by tasting panels. Ethanol vapours reduced Botrytis rot incidence and berry shatter, but hastened stem browning. Sensory analyses did not detect any differences between treatments

Radial Velocity Variations in Pulsating Ap Stars III. The Discovery of 16.21 min Oscillations in Beta CrB

We present the analysis of 3 hrs of a rapid time series of precise stellar radial velocity (RV) measurements (sigma = 4.5 m/s) of the cool Ap star Beta CrB. The integrated RV measurements spanning the wavelength interval 5000-6000 Ang. show significant variations (false alarm probability = 10^-5) with a period of 16.21 min (nu = 1028.17 micro Hz) and an amplitude of 3.54 +/- 0.56 m/s. The RV measured over a much narrower wavelength interval reveals one spectral feature at 6272 Ang. pulsating with the same 16.21 min period and an amplitude of 138 +/- 23 m/s. These observations establish Beta CrB to be a low-amplitude rapidly oscillating Ap star.Comment: 5 Pages, 5 figure

Bohmian arrival time without trajectories

The computation of detection probabilities and arrival time distributions within Bohmian mechanics in general needs the explicit knowledge of a relevant sample of trajectories. Here it is shown how for one-dimensional systems and rigid inertial detectors these quantities can be computed without calculating any trajectories. An expression in terms of the wave function and its spatial derivative, both restricted to the boundary of the detector's spacetime volume, is derived for the general case, where the probability current at the detector's boundary may vary its sign.Comment: 20 pages, 12 figures; v2: reference added, extended introduction, published versio

MOST observations of the roAp stars HD 9289, HD 99563, and HD 134214

We report on the analysis of high-precision space-based photometry of the roAp (rapidly oscillating Ap) stars HD 9289, HD 99563, and HD134214. All three stars were observed by the MOST satellite for more than 25 days, allowing unprecedented views of their pulsation. We find previously unknown candidate frequencies in all three stars. We establish the rotation period of HD 9289 (8.5 d) for the first time and show that the star is pulsating in two modes that show different mode geometries. We present a detailed analysis of HD 99563's mode multiplet and find a new candidate frequency which appears independent of the previously known mode. Finally, we report on 11 detected pulsation frequencies in HD 134214, 9 of which were never before detected in photometry, and 3 of which are completely new detections. Thanks to the unprecedentedly small frequency uncertainties, the p-mode spectrum of HD 134214 can be seen to have a well-defined large frequency spacing similar to the well-studied roAp star HD 24712 (HR 1217).Comment: 11 pages, 12 figures, accepted for publication in A&

HV/HR-CMOS sensors for the ATLAS upgrade—concepts and test chip results

In order to extend its discovery potential, the Large Hadron Collider (LHC) will have a major upgrade (Phase II Upgrade) scheduled for 2022. The LHC after the upgrade, called High-Luminosity LHC (HL-LHC), will operate at a nominal leveled instantaneous luminosity of 5× 1034 cm−2 s−1, more than twice the expected Phase I . The new Inner Tracker needs to cope with this extremely high luminosity. Therefore it requires higher granularity, reduced material budget and increased radiation hardness of all components. A new pixel detector based on High Voltage CMOS (HVCMOS) technology targeting the upgraded ATLAS pixel detector is under study. The main advantages of the HVCMOS technology are its potential for low material budget, use of possible cheaper interconnection technologies, reduced pixel size and lower cost with respect to traditional hybrid pixel detector. Several first prototypes were produced and characterized within ATLAS upgrade R&D effort, to explore the performance and radiation hardness of this technology. In this paper, an overview of the HVCMOS sensor concepts is given. Laboratory tests and irradiation tests of two technologies, HVCMOS AMS and HVCMOS GF, are also given