Thermodynamic identities and particle number fluctuations in weakly interacting Bose--Einstein condensates

We derive exact thermodynamic identities relating the average number of condensed atoms and the root-mean-square fluctuations determined in different statistical ensembles for the weakly interacting Bose gas confined in a box. This is achieved by introducing the concept of {\it auxiliary partition functions} for model Hamiltonians that do conserve the total number of particles. Exploiting such thermodynamic identities, we provide the first, completely analytical prediction of the microcanonical particle number fluctuations in the weakly interacting Bose gas. Such fluctuations, as a function of the volume V of the box are found to behave normally, at variance with the anomalous scaling behavior V^{4/3} of the fluctuations in the ideal Bose gas.Comment: 5 pages, 1 figur

Quantized Roentgen Effect in Bose-Einstein Condensates

A classical dielectric moving in a charged capacitor can create a magnetic field (Roentgen effect). A quantum dielectric, however, will not produce a magnetization, except at vortices. The magnetic field outside the quantum dielectric appears as the field of quantized monopoles

Determination of Shear Wave Velocity and Attenuation From Waveforms in Low Velocity Formations

In boreholes where formation shear velocity is lower than borehole fluid velocity neither refracted shear waves nor pseudo-Rayleigh waves can propagate. When frequency response of the sonde does not extend to low frequencies (e.g. 2 kHz) Stoneley waves are not excited efficiently. In such cases refracted P, leaking modes (PL) and fluid waves become dominant phases on a full waveform acoustic log. The P wave velocity can be determined from the first arrivals. Then, using synthetic microseismograms and a waveform matching technique, formation shear wave velocity and attenuation can be determined. This method· is demonstrated using data from a well in the Baltimore Canyon Trough area of the Atlantic margin.Massachusetts Institute of Technology. Full Waveform Acoustic Logging Consortiu

Local/Non-Local Complementarity in Topological Effects

In certain topological effects the accumulation of a quantum phase shift is accompanied by a local observable effect. We show that such effects manifest a complementarity between non-local and local attributes of the topology, which is reminiscent but yet different from the usual wave-particle complementarity. This complementarity is not a consequence of non-commutativity, rather it is due to the non-canonical nature of the observables. We suggest that a local/non-local complementarity is a general feature of topological effects that are ``dual'' to the AB effect.Comment: 4 page

Mesoscopic Fermi gas in a harmonic trap

We study the thermodynamical properties of a mesoscopic Fermi gas in view of recent possibilities to trap ultracold atoms in a harmonic potential. We focus on the effects of shell closure for finite small atom numbers. The dependence of the chemical potential, the specific heat and the density distribution on particle number and temperature is obtained. Isotropic and anisotropic traps are compared. Possibilities of experimental observations are discussed.Comment: 8 pages, 9 eps-figures included, Revtex, submitted to Phys. Rev. A, minor changes to figures and captions, corrected typo

Physical Properties of a Set of Sandstones, III: the Effects Of Fine Grained Pore Filling Material on Compressional Wave Velocity

We have used aspect ratio modeling to explain the measured compressional wave velocities of twenty different dry sandstone samples with varying clay contents at a single confining pressure of 0.5 kbar. Velocities of the sandstones range between 3.1 km/sec and 5.7 km/sec. Measured porosities are between 6% and 33%, clay contents between 2% and 30%. Pores were described using three simple type classifications. The pore type distributions of the samples were quantified by point counting polished impregnated thin sections using a scanning electron microscope. A representative aspect-ratio was assigned to each of the three categories of pore type. Velocities were modeled using these aspect ratios weighted by the observed distribution of the porosity types. Agreement between theoretical and measured velocities is generally within 10%. The modeling suggests that the effects of clays in sandstone pores is to reduce the sample porosity without reducing the non-framework (void + clay) volume. Thus, for a given porosity, clay rich samples contain greater non-framework volume, which in turn lowers velocity. The model derived from the dry measurements can be used to successfully approximate empirical relationships for saturated samples of velocity-porosity-clay content taken from the literature.Schlumberger-Doll Research CenterSchlumberger Foundation. Post-Doctoral Fellowshi

Are Homeschoolers Prepared for College Calculus?

Homeschooling in the United States has grown considerably over the past several decades. This article presents findings from the Factors Influencing College Success in Mathematics (FICSMath) survey, a national study of 10,492 students enrolled in tertiary calculus, including 190 students who reported homeschooling for a majority of their high school years. The authors found that, compared with students who received other types of secondary schooling, students who homeschooled: (a) were demographically similar to their peers, (b) earned similar SAT Math scores, and (c) earned higher tertiary calculus grades

High School Prpearation for College Calculus: Is the Story the Same for Males and Females?

Usingdatafromthefirst national study on high schoolpreparationfor college calculus, the Factors Including College Success in Mathematics (FICSMath) project, this paper connects males’ (n53,648) and females’ (n52,033) instructional experiences from their high school precalculus or calculus course to their college calculus performance. A hierarchical linear model identifies several significant instructional experiences that predict college calculus performance. Our findings show that high school instructional practices affect college calculus performance similarly for males and females

X-ray diffraction peak profiles from threading dislocations in GaN epitaxial films

We analyze the lineshape of x-ray diffraction profiles of GaN epitaxial layers with large densities of randomly distributed threading dislocations. The peaks are Gaussian only in the central, most intense part of the peak, while the tails obey a power law. The $q^{-3}$ decay typical for random dislocations is observed in double-crystal rocking curves. The entire profile is well fitted by a restricted random dislocation distribution. The densities of both edge and screw threading dislocations and the ranges of dislocation correlations are obtained

Transition temperature of a dilute homogeneous imperfect Bose gas

The leading-order effect of interactions on a homogeneous Bose gas is theoretically predicted to shift the critical temperature by an amount \Delta\Tc = # a_{scatt} n^{1/3} T_0 from the ideal gas result T_0, where a_{scatt} is the scattering length and n is the density. There have been several different theoretical estimates for the numerical coefficient #. We claim to settle the issue by measuring the numerical coefficient in a lattice simulation of O(2) phi^4 field theory in three dimensions---an effective theory which, as observed previously in the literature, can be systematically matched to the dilute Bose gas problem to reproduce non-universal quantities such as the critical temperature. We find # = 1.32 +- 0.02.Comment: 4 pages, submitted to Phys. Rev. Lett; minor changes due to improvement of analysis in the longer companion pape