On the uncertainty relations and squeezed states for the quantum mechanics on a circle

The uncertainty relations for the position and momentum of a quantum particle on a circle are identified minimized by the corresponding coherent states. The sqeezed states in the case of the circular motion are introduced and discussed in the context of the uncertainty relations.Comment: 4 figure

Toward a numerical deshaker for PFS

The Planetary Fourier Spectrometer (PFS) onboard Mars Express (MEx) is the instrument with the highest spectral resolution observing Mars from orbit since January 2004. It permits studying the atmospheric structure, major and minor compounds. The present time version of the calibration is limited by the effects of mechanical vibration, currently not corrected. We proposed here a new approach to correct for the vibrations based on semi-blind deconvolution of the measurements. This new approach shows that a correction can be done efficiently with 85% reduction of the artefacts, in a equivalent manner to the stacking of 10 spectra. Our strategy is not fully automatic due to the dependence on some regularisation parameters. It may be applied on the complete PFS dataset, correcting the large-scale perturbation due to microvibrations for each spectrum independently. This approach is validated on actual PFS data of Short Wavelength Channel (SWC), perturbed by microvibrations. A coherence check can be performed and also validate our approach. Unfortunately, the coherence check can be done only on the first 310 orbits of MEx only, until the laser line has been switch off. More generally, this work may apply to numerically "deshake" Fourier Transform Spectrometer (FTS), widely used in space experiments or in the laboratory.Comment: 18 pages, 8 figures, submitted to Planetary and Space Scienc

MnAs dots grown on GaN(0001)-(1x1) surface

MnAs has been grown by means of MBE on the GaN(0001)-(1x1) surface. Two options of initiating the crystal growth were applied: (a) a regular MBE procedure (manganese and arsenic were delivered simultaneously) and (b) subsequent deposition of manganese and arsenic layers. It was shown that spontaneous formation of MnAs dots with the surface density of 1$\cdot 10^{11}$ cm$^{-2}$ and $2.5\cdot 10^{11}$ cm$^{-2}$, respectively (as observed by AFM), occurred for the layer thickness higher than 5 ML. Electronic structure of the MnAs/GaN systems was studied by resonant photoemission spectroscopy. That led to determination of the Mn 3d - related contribution to the total density of states (DOS) distribution of MnAs. It has been proven that the electronic structures of the MnAs dots grown by the two procedures differ markedly. One corresponds to metallic, ferromagnetic NiAs-type MnAs, the other is similar to that reported for half-metallic zinc-blende MnAs. Both system behave superparamagnetically (as revealed by magnetization measurements), but with both the blocking temperatures and the intra-dot Curie temperatures substantially different. The intra-dot Curie temperature is about 260 K for the former system while markedly higher than room temperature for the latter one. Relations between growth process, electronic structure and other properties of the studied systems are discussed. Possible mechanisms of half-metallic MnAs formation on GaN are considered.Comment: 20+ pages, 8 figure

Curvature homogeneous spacelike Jordan Osserman pseudo-Riemannian manifolds

Let s be at least 2. We construct Ricci flat pseudo-Riemannian manifolds of signature (2s,s) which are not locally homogeneous but whose curvature tensors never the less exhibit a number of important symmetry properties. They are curvature homogeneous; their curvature tensor is modeled on that of a local symmetric space. They are spacelike Jordan Osserman with a Jacobi operator which is nilpotent of order 3; they are not timelike Jordan Osserman. They are k-spacelike higher order Jordan Osserman for $2\le k\le s$; they are k-timelike higher order Jordan Osserman for $s+2\le k\le 2s$, and they are not k timelike higher order Jordan Osserman for $2\le s\le s+1$.Comment: Update bibliography, fix minor misprint

Coherent states on spheres

We describe a family of coherent states and an associated resolution of the identity for a quantum particle whose classical configuration space is the d-dimensional sphere S^d. The coherent states are labeled by points in the associated phase space T*(S^d). These coherent states are NOT of Perelomov type but rather are constructed as the eigenvectors of suitably defined annihilation operators. We describe as well the Segal-Bargmann representation for the system, the associated unitary Segal-Bargmann transform, and a natural inversion formula. Although many of these results are in principle special cases of the results of B. Hall and M. Stenzel, we give here a substantially different description based on ideas of T. Thiemann and of K. Kowalski and J. Rembielinski. All of these results can be generalized to a system whose configuration space is an arbitrary compact symmetric space. We focus on the sphere case in order to be able to carry out the calculations in a self-contained and explicit way.Comment: Revised version. Submitted to J. Mathematical Physic

Two-species magneto-optical trap with 40K and 87Rb

We trap and cool a gas composed of 40K and 87Rb, using a two-species magneto-optical trap (MOT). This trap represents the first step towards cooling the Bose-Fermi mixture to quantum degeneracy. Laser light for the MOT is derived from laser diodes and amplified with a single high power semiconductor amplifier chip. The four-color laser system is described, and the single-species and two-species MOTs are characterized. Atom numbers of 1x10^7 40K and 2x10^9 87Rb are trapped in the two-species MOT. Observation of trap loss due to collisions between species is presented and future prospects for the experiment are discussed.Comment: 4 pages, 4 figures; accepted for publication in Physical Review

Effective area calibration of the reflection grating spectrometers of XMM-Newton. II. X-ray spectroscopy of DA white dwarfs

White dwarf spectra have been widely used as a calibration source for X-ray and EUV instruments. The in-flight effective area calibration of the reflection grating spectrometers (RGS) of XMM-Newton depend upon the availability of reliable calibration sources. We investigate how well these white dwarf spectra can be used as standard candles at the lowest X-ray energies in order to gauge the absolute effective area scale of X-ray instruments. We calculate a grid of model atmospheres for Sirius B and HZ 43A, and adjust the parameters using several constraints until the ratio of the spectra of both stars agrees with the ratio as observed by the low energy transmission grating spectrometer (LETGS) of Chandra. This ratio is independent of any errors in the effective area of the LETGS. We find that we can constrain the absolute X-ray spectrum of both stars with better than 5 % accuracy. The best-fit model for both stars is close to a pure hydrogen atmosphere, and we put tight limits to the amount of helium or the thickness of a hydrogen layer in both stars. Our upper limit to the helium abundance in Sirius B is 4 times below the previous detection based on EUVE data. We also find that our results are sensitive to the adopted cut-off in the Lyman pseudo-continuum opacity in Sirius B. We get best agreement with a long wavelength cut-off. White dwarf model atmospheres can be used to derive the effective area of X-ray spectrometers in the lowest energy band. An accuracy of 3-4 % in the absolute effective area can be achieved.Comment: 15 pages, 7 figures, accepted for publication in Astronomy & Astrophysics, main journa

Complete curvature homogeneous pseudo-Riemannian manifolds

We exhibit 3 families of complete curvature homogeneous pseudo-Riemannian manifolds which are modeled on irreducible symmetric spaces and which are not locally homogeneous. All of the manifolds have nilpotent Jacobi operators; some of the manifolds are, in addition, Jordan Osserman and Jordan Ivanov-Petrova.Comment: Update paper to fix misprints in original versio