Scarred eigenstates for quantum cat maps of minimal periods

In this paper we construct a sequence of eigenfunctions of the ``quantum Arnold's cat map'' that, in the semiclassical limit, show a strong scarring phenomenon on the periodic orbits of the dynamics. More precisely, those states have a semiclassical limit measure that is the sum of 1/2 the normalized Lebesgue measure on the torus plus 1/2 the normalized Dirac measure concentrated on any a priori given periodic orbit of the dynamics. It is known (the Schnirelman theorem) that ``most'' sequences of eigenfunctions equidistribute on the torus. The sequences we construct therefore provide an example of an exception to this general rule. Our method of construction and proof exploits the existence of special values of Planck's constant for which the quantum period of the map is relatively ``short'', and a sharp control on the evolution of coherent states up to this time scale. We also provide a pointwise description of these states in phase space, which uncovers their ``hyperbolic'' structure in the vicinity of the fixed points and yields more precise localization estimates.Comment: LaTeX, 49 pages, includes 10 figures. I added section 6.6. To be published in Commun. Math. Phy

Near threshold rotational excitation of molecular ions by electron-impact

New cross sections for the rotational excitation of H$_3^+$ by electrons are calculated {\it ab initio} at low impact energies. The validity of the adiabatic-nuclei-rotation (ANR) approximation, combined with $R$-matrix wavefunctions, is assessed by comparison with rovibrational quantum defect theory calculations based on the treatment of Kokoouline and Greene ({\it Phys. Rev. A} {\bf 68} 012703 2003). Pure ANR excitation cross sections are shown to be accurate down to threshold, except in the presence of large oscillating Rydberg resonances. These resonances occur for transitions with $\Delta J=1$ and are caused by closed channel effects. A simple analytic formula is derived for averaging the rotational probabilities over such resonances in a 3-channel problem. In accord with the Wigner law for an attractive Coulomb field, rotational excitation cross sections are shown to be large and finite at threshold, with a significant but moderate contribution from closed channels.Comment: 3 figures, a5 page

Experiments with a fully instrumented split Stirling cryocooler

A practical model that can be used to accurately size and optimally split stirling cryocoolers is discussed. A practical model that could be used to extrapolate existing designs to meet different specifications was developed. However, to do this detailed knowledge of the dynamic operating parameters of this type of cryocooler is required. The first stage is to fully instrument a refrigerator so that various dynamic parameters can be measured. The second stage involves the application of these measurements to the design and optimization of a range of coolers

A seven square degrees survey for galaxy-scale gravitational lenses with the HST imaging archive

We present the results of a visual search for galaxy-scale gravitational lenses in nearly 7 square degrees of Hubble Space Telescope (HST) images. The dataset comprises the whole imaging data ever taken with the Advanced Camera for Surveys (ACS) in the filter F814W (I-band) up to August 31st, 2011, i.e. 6.03 square degrees excluding the field of the Cosmic Evolution Survey (COSMOS) which has been the subject of a separate visual search. In addition, we have searched for lenses in the whole Wide Field Camera 3 (WFC3) near-IR imaging dataset in all filters (1.01 square degrees) up to the same date. Our primary goal is to provide a sample of lenses with a broad range of different morphologies and lens-source brightness contrast in order estimate a lower limit to the number of galaxy-scale strong lenses in the future Euclid survey in its VIS band. Our criteria to select lenses are purely morphological as we do not use any colour or redshift information.The final candidate selection is very conservative hence leading to a nearly pure but incomplete sample. We find 49 new lens candidates: 40 in the ACS images and 9 in the WFC3 images. Out of these, 16 candidates are secure lenses owing to their striking morphology, 21 more are very good candidates, and 12 more have morphologies compatible with gravitational lensing but also compatible with other astrophysical objects. It is therefore insensitive to cosmic variance and allows to estimate the number of galaxy-scale strong lenses on the sky for a putative survey depth, which is the main result of the present work. Because of the incompleteness of the sample, the estimated lensing rates should be taken as lower limits. Using these, we anticipate that a 15 000 square degrees space survey such as Euclid will find at least 60 000 galaxy-scale strong lenses down to a limiting AB magnitude of I = 24.5 (10-sigma) or I = 25.8 (3-sigma).Comment: 13 pages, 12 figures, Accepted for publication in MNRA

Upper bound on the density of Ruelle resonances for Anosov flows

Using a semiclassical approach we show that the spectrum of a smooth Anosov vector field V on a compact manifold is discrete (in suitable anisotropic Sobolev spaces) and then we provide an upper bound for the density of eigenvalues of the operator (-i)V, called Ruelle resonances, close to the real axis and for large real parts.Comment: 57 page

Feldspar-Provenance Dates in a Stratigraphic Section of Till in Gahanna, Ohio

Author Institution: Department of Geology and Mineralogy and The Institute of Polar Studies, The Ohio State UniversityThe internal layering and provenance of feldspar in 3 tills and in one outwash deposit at Gahanna, Ohio, were studied by determining pebble lithologies and Rb-Sr dates of feldspar. Variations in lithology of pebbles and in the Rb-Sr ratios of feldspar in the 125—250 micrometer fractions reveal discontinuities which divide the upper 2 tills into 2 subunits each. Each of the lower subunits appears to be more homogeneous than the upper ones based on comparisons of standard deviations. This suggests the lower subunits may be basal or lodgement till and the upper subunits may be ablation till. Feldspar-provenance dates in till of the mid western United States are expressions of the proportion of mixing of feldspar grains originating from the Superior (2.7 b. y.) and Grenville (1.07 b. y.) structural provinces of the Canadian Precambrian Shield. The Rb-Sr dates of feldspar in the layers of till and outwash of the Gahanna section are so variable that average dates cannot be used to distinguish among them. The lack of systematic stratigraphic variation of provenance dates indicates the feldspars are heterogeneous mixtures of the two Precambrian components. Approximately 90% of the dates have values between 1.0 and 1.5 b.y., which demonstrates the dominance of feldspar derived from the Grenville Province. Four samples whose dates are less than 1.0 b. y. contain younger feldspar presumably derived from sandstone of late Paleozoic age

The magnetic precursor of L1448-mm: Excitation differences between ion and neutral fluids

Shock modelling predicts an electron density enhancement within the magnetic precursor of C-shocks. Previous observations of SiO, H13CO+, HN13C and H13CN toward the young L1448-mm outflow showed an over-excitation of the ion fluid that was attributed to an electron density enhancement in the precursor. We re-visit this interpretation and test if it still holds when we consider different source morphologies and kinetic temperatures for the observed molecules, and also give some insight on the spatial extent of the electron density enhancement around L1448-mm. We estimate the opacities of H13CO+ and HN13C by observing the J=3\to2 lines of rarer isotopologues to confirm that the emission is optically thin. To model the excitation of the molecules, we use the large velocity gradient (LVG) approximation with updated collisional coefficients to i) re- analyse the observations toward the positions where the over-excitation of H13CO+ has previously been observed [i.e. toward L1448- mm at offsets (0,0) and (0,-10)], and ii) to investigate if the electron density enhancement is still required for the cases of extended and compact emission, and for kinetic temperatures of up to 400 K. We also report several lines of SiO, HN13C and H13CO+ toward new positions around this outflow, to investigate the spatial extent of the over-excitation of the ions in L1448-mm. From the isotopologue observations, we find that the emission of H13CO+ and HN13C from the precursor is optically thin if this emission is extended. Using the new collisional coefficients, an electron density enhancement is still needed to explain the excitation of H13CO+ for extended emission and for gas temperatures of\le 400 K toward L1448-mm (0,-10), and possibly also toward L1448-mm (0,0). For compact emission the data cannot be fitted. We do not find any evidence for the over-excitation of the ion fluid toward the newly observed positions around L1448-mm. The observed line emission of SiO, H13CO+ and HN13C toward L1448-mm (0,0) and (0,-10) is consistent with an electron density enhancement in the precursor component, if this emission is spatially extended. This is also true for the case of high gas temperatures (\le400 K) toward the (0,-10) offset. The electron density enhancement seems to be restricted to the southern, redshifted lobe of the L1448-mm outflow. Interferometric images of the line emission of these molecules are needed to confirm the spatial extent of the over-excitation of the ions and thus, of the electron density enhancement in the magnetic precursor of L1448-mm.Comment: Accepted for publication in A&A; 9 pages, 3 figure