Sets avoided by Brownian motion

Any fixed cylinder is hit almost surely by a 3-dimensional Brownian motion, but is there a random cylinder that is in the complement? We answer this for cylinders, and then replacing a cylinder with a more general set

Quasi integral of motion for axisymmetric potentials

We present an estimate of the third integral of motion for axisymmetric three-dimensional potentials. This estimate is based on a Staeckel approximation and is explicitly written as a function of the potential. We tested this scheme for the Besancon Galactic model and two other disc-halo models and find that orbits of disc stars have an accurately conserved third quasi integral. The accuracy ranges from of 0.1% to 1% for heights varying from z = 0~kpc to z= 6 kpc and Galactocentric radii R from 5 to 15kpc. We also tested the usefulness of this quasi integral in analytic distribution functions of disc stellar populations: we show that the distribution function remains approximately stationary and that it allows to recover the potential and forces by applying Jeans equations to its moments.Comment: 9 pages, 9 figures, accepted for publication in Astron. and Astrophy

Subradiance in a Large Cloud of Cold Atoms

Since Dicke's seminal paper on coherence in spontaneous radiation by atomic ensembles, superradiance has been extensively studied. Subradiance, on the contrary, has remained elusive, mainly because subradiant states are weakly coupled to the environment and are very sensitive to nonradiative decoherence processes.Here we report the experimental observation of subradiance in an extended and dilute cold-atom sample containing a large number of particles. We use a far detuned laser to avoid multiple scattering and observe the temporal decay after a sudden switch-off of the laser beam. After the fast decay of most of the fluorescence, we detect a very slow decay, with time constants as long as 100 times the natural lifetime of the excited state of individual atoms. This subradiant time constant scales linearly with the cooperativity parameter, corresponding to the on-resonance optical depth of the sample, and is independent of the laser detuning, as expected from a coupled-dipole model

Superradiance in a Large and Dilute Cloud of Cold Atoms in the Linear-Optics Regime

Superradiance has been extensively studied in the 1970s and 1980s in the regime of superfluores-cence, where a large number of atoms are initially excited. Cooperative scattering in the linear-optics regime, or "single-photon superradiance" , has been investigated much more recently, and superra-diant decay has also been predicted, even for a spherical sample of large extent and low density, where the distance between atoms is much larger than the wavelength. Here, we demonstrate this effect experimentally by directly measuring the decay rate of the off-axis fluorescence of a large and dilute cloud of cold rubidium atoms after the sudden switch-off of a low-intensity laser driving the atomic transition. We show that, at large detuning, the decay rate increases with the on-resonance optical depth. In contrast to forward scattering, the superradiant decay of off-axis fluorescence is suppressed near resonance due to attenuation and multiple-scattering effects

New surveys of UBV photometry and absolute proper motions at intermediate latitude

A photometric and proper motion survey has been obtained in 2 directions at intermediate latitude: ($l=167.5^\circ$, $b=47.4^\circ$; $\alpha_{2000}=9^h41^m26^s$,$\delta_{2000}=+49^\circ53'27''$) and ($l=278^\circ$, $b=47^\circ$; $\alpha_{2000}=11^h42^m56^s$, $\delta_{2000}=-12^\circ31'42''$). The survey covers 7.13 and 20.84 square degrees, respectively. The limiting magnitude is about 18.5 in V for both directions. We have derived the density laws for stars (M$_{V}$ $\ge$ 3.5) as a function of distance from the galactic plane. The density laws for stars follow a sum of two exponentials with scale heights of 240 pc (thin disk) and 790 pc (thick disk), respectively. The local density of thick disk is found to be 6.1$\pm$3 % relative to the thin disk. The kinematical distribution of stars has been probed to distances up to 3.5 kpc above the galactic plane. New estimates of the parameters of velocity ellipsoid have been derived for the thick disk of the Galaxy. A comparison of our data sets with the Besan\c con model star count predictions has been performed, giving a good agreement in the magnitude range V = 13 to 18.Comment: 13 pages, 8 PS figures, To appear in A&

Entanglement verification with finite data

Suppose an experimentalist wishes to verify that his apparatus produces entangled quantum states. A finite amount of data cannot conclusively demonstrate entanglement, so drawing conclusions from real-world data requires statistical reasoning. We propose a reliable method to quantify the weight of evidence for (or against) entanglement, based on a likelihood ratio test. Our method is universal in that it can be applied to any sort of measurements. We demonstrate the method by applying it to two simulated experiments on two qubits. The first measures a single entanglement witness, while the second performs a tomographically complete measurement.Comment: 4 pages, 3 pretty picture

Do Spellings of Words and Phonemic Awareness Training Facilitate Vocabulary Learning in Preschoolers?

The purpose of this study was to examine the contribution of phoneme awareness training and orthography to the learning of new vocabulary words by partial alphabetic phase readers. We hypothesized that four and five year old children taught to segment words with letters would outperform those trained with shape markers and those that received no segmentation training on an invented spelling task. We also hypothesized that students seeing the spellings of new vocabulary words (names) would learn the words in fewer trials, remember the names and features better and would be able to better recognize letter labels when presented alone. An experimental counterbalanced design was used. Children were screened to select readers in the partial alphabetic phase. They were assigned randomly to one of three conditions. Children were given training in phonemic awareness by learning to segment simple words with letter markers or shape markers. A third control condition was read a rhyming book and no segmentation was taught. Children were then taught new vocabulary words naming interesting and unusual drawings of characters. Half of the drawings were accompanied by simple consonant-vowel spellings symbolizing their names and half by unrelated two-digit numbers in a repeated measures design. Students were given up to 20 learning trials with corrective feedback to learn the picture-name associations. Results indicated that children who received phonemic segmentation training with letters made significant gains from pretest to posttest in producing simplified spellings of words whereas the other two groups who were not trained with letters showed no improvement. In the vocabulary learning task, results revealed that when participants were shown spellings of the words during study periods but not during tests, they required fewer trials to learn the words than when they were shown irrelevant numbers. Phonemic segmentation training with letters did not improve vocabulary learning compared to training without letters or rhyme training. Findings showed that beginning readers’ memory for vocabulary words can be facilitated when they are exposed to spellings of the words, even beginners in the partial alphabetic phase of reading development. Knowledge of letter names containing the relevant sounds in their names appeared to be sufficient to support facilitation of vocabulary learning from spellings but training in phoneme segmentation provided no additional benefit