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

Wrangling environmental exposure data: guidance for getting the best information from your laboratory measurements.

BACKGROUND:Environmental health and exposure researchers can improve the quality and interpretation of their chemical measurement data, avoid spurious results, and improve analytical protocols for new chemicals by closely examining lab and field quality control (QC) data. Reporting QC data along with chemical measurements in biological and environmental samples allows readers to evaluate data quality and appropriate uses of the data (e.g., for comparison to other exposure studies, association with health outcomes, use in regulatory decision-making). However many studies do not adequately describe or interpret QC assessments in publications, leaving readers uncertain about the level of confidence in the reported data. One potential barrier to both QC implementation and reporting is that guidance on how to integrate and interpret QC assessments is often fragmented and difficult to find, with no centralized repository or summary. In addition, existing documents are typically written for regulatory scientists rather than environmental health researchers, who may have little or no experience in analytical chemistry. OBJECTIVES:We discuss approaches for implementing quality assurance/quality control (QA/QC) in environmental exposure measurement projects and describe our process for interpreting QC results and drawing conclusions about data validity. DISCUSSION:Our methods build upon existing guidance and years of practical experience collecting exposure data and analyzing it in collaboration with contract and university laboratories, as well as the Centers for Disease Control and Prevention. With real examples from our data, we demonstrate problems that would not have come to light had we not engaged with our QC data and incorporated field QC samples in our study design. Our approach focuses on descriptive analyses and data visualizations that have been compatible with diverse exposure studies with sample sizes ranging from tens to hundreds of samples. Future work could incorporate additional statistically grounded methods for larger datasets with more QC samples. CONCLUSIONS:This guidance, along with example table shells, graphics, and some sample R code, provides a useful set of tools for getting the best information from valuable environmental exposure datasets and enabling valid comparison and synthesis of exposure data across studies