Quantum correlations and spatial localization in one-dimensional ultracold bosonic mixtures

We present the complete phase diagram for one-dimensional binary mixtures of bosonic ultracold atomic gases in a harmonic trap. We obtain exact results with direct numerical diagonalization for small number of atoms, which permits us to quantify quantum many-body correlations. The quantum Monte Carlo method is used to calculate energies and density profiles for larger system sizes. We study the system properties for a wide range of interaction parameters. For the extreme values of these parameters, different correlation limits can be identified, where the correlations are either weak or strong. We investigate in detail how the correlation evolve between the limits. For balanced mixtures in the number of atoms in each species, the transition between the different limits involves sophisticated changes in the one- and two-body correlations. Particularly, we quantify the entanglement between the two components by means of the von Neumann entropy. We show that the limits equally exist when the number of atoms is increased, for balanced mixtures. Also, the changes in the correlations along the transitions among these limits are qualitatively similar. We also show that, for imbalanced mixtures, the same limits with similar transitions exist. Finally, for strongly imbalanced systems, only two limits survive, i.e., a miscible limit and a phase-separated one, resembling those expected with a mean-field approach.Comment: 18 pages, 8 figure

Kinetic Energy Density Study of Some Representative Semilocal Kinetic Energy Functionals

There is a number of explicit kinetic energy density functionals for non-interacting electron systems that are obtained in terms of the electron density and its derivatives. These semilocal functionals have been widely used in the literature. In this work we present a comparative study of the kinetic energy density of these semilocal functionals, stressing the importance of the local behavior to assess the quality of the functionals. We propose a quality factor that measures the local differences between the usual orbital-based kinetic energy density distributions and the approximated ones, allowing to ensure if the good results obtained for the total kinetic energies with these semilocal functionals are due to their correct local performance or to error cancellations. We have also included contributions coming from the laplacian of the electron density to work with an infinite set of kinetic energy densities. For all the functionals but one we have found that their success in the evaluation of the total kinetic energy are due to global error cancellations, whereas the local behavior of their kinetic energy density becomes worse than that corresponding to the Thomas-Fermi functional.Comment: 12 pages, 3 figure

Distinguishability, degeneracy and correlations in three harmonically trapped bosons in one-dimension

We study a system of two bosons of one species and a third boson of a second species in a one-dimensional parabolic trap at zero temperature. We assume contact repulsive inter- and intra-species interactions. By means of an exact diagonalization method we calculate the ground and excited states for the whole range of interactions. We use discrete group theory to classify the eigenstates according to the symmetry of the interaction potential. We also propose and validate analytical ansatzs gaining physical insight over the numerically obtained wavefunctions. We show that, for both approaches, it is crucial to take into account that the distinguishability of the third atom implies the absence of any restriction over the wavefunction when interchanging this boson with any of the other two. We find that there are degeneracies in the spectra in some limiting regimes, that is, when the inter-species and/or the intra-species interactions tend to infinity. This is in contrast with the three-identical boson system, where no degeneracy occurs in these limits. We show that, when tuning both types of interactions through a protocol that keeps them equal while they are increased towards infinity, the systems's ground state resembles that of three indistinguishable bosons. Contrarily, the systems's ground state is different from that of three-identical bosons when both types of interactions are increased towards infinity through protocols that do not restrict them to be equal. We study the coherence and correlations of the system as the interactions are tuned through different protocols, which permit to built up different correlations in the system and lead to different spatial distributions of the three atoms.Comment: 14 pages, 7 figure

Classical kinetic energy, quantum fluctuation terms and kinetic-energy functionals

We employ a recently formulated dequantization procedure to obtain an exact expression for the kinetic energy which is applicable to all kinetic-energy functionals. We express the kinetic energy of an N-electron system as the sum of an N-electron classical kinetic energy and an N-electron purely quantum kinetic energy arising from the quantum fluctuations that turn the classical momentum into the quantum momentum. This leads to an interesting analogy with Nelson's stochastic approach to quantum mechanics, which we use to conceptually clarify the physical nature of part of the kinetic-energy functional in terms of statistical fluctuations and in direct correspondence with Fisher Information Theory. We show that the N-electron purely quantum kinetic energy can be written as the sum of the (one-electron) Weizsacker term and an (N-1)-electron kinetic correlation term. We further show that the Weizsacker term results from local fluctuations while the kinetic correlation term results from the nonlocal fluctuations. For one-electron orbitals (where kinetic correlation is neglected) we obtain an exact (albeit impractical) expression for the noninteracting kinetic energy as the sum of the classical kinetic energy and the Weizsacker term. The classical kinetic energy is seen to be explicitly dependent on the electron phase and this has implications for the development of accurate orbital-free kinetic-energy functionals. Also, there is a direct connection between the classical kinetic energy and the angular momentum and, across a row of the periodic table, the classical kinetic energy component of the noninteracting kinetic energy generally increases as Z increases.Comment: 10 pages, 1 figure. To appear in Theor Chem Ac

Astrometric calibration and performance of the Dark Energy Camera

We characterize the ability of the Dark Energy Camera (DECam) to perform relative astrometry across its 500~Mpix, 3 deg^2 science field of view, and across 4 years of operation. This is done using internal comparisons of ~4x10^7 measurements of high-S/N stellar images obtained in repeat visits to fields of moderate stellar density, with the telescope dithered to move the sources around the array. An empirical astrometric model includes terms for: optical distortions; stray electric fields in the CCD detectors; chromatic terms in the instrumental and atmospheric optics; shifts in CCD relative positions of up to ~10 um when the DECam temperature cycles; and low-order distortions to each exposure from changes in atmospheric refraction and telescope alignment. Errors in this astrometric model are dominated by stochastic variations with typical amplitudes of 10-30 mas (in a 30 s exposure) and 5-10 arcmin coherence length, plausibly attributed to Kolmogorov-spectrum atmospheric turbulence. The size of these atmospheric distortions is not closely related to the seeing. Given an astrometric reference catalog at density ~0.7 arcmin^{-2}, e.g. from Gaia, the typical atmospheric distortions can be interpolated to 7 mas RMS accuracy (for 30 s exposures) with 1 arcmin coherence length for residual errors. Remaining detectable error contributors are 2-4 mas RMS from unmodelled stray electric fields in the devices, and another 2-4 mas RMS from focal plane shifts between camera thermal cycles. Thus the astrometric solution for a single DECam exposure is accurate to 3-6 mas (0.02 pixels, or 300 nm) on the focal plane, plus the stochastic atmospheric distortion.Comment: Submitted to PAS

Forward Global Photometric Calibration of the Dark Energy Survey

Many scientific goals for the Dark Energy Survey (DES) require calibration of optical/NIR broadband $b = grizY$ photometry that is stable in time and uniform over the celestial sky to one percent or better. It is also necessary to limit to similar accuracy systematic uncertainty in the calibrated broadband magnitudes due to uncertainty in the spectrum of the source. Here we present a "Forward Global Calibration Method (FGCM)" for photometric calibration of the DES, and we present results of its application to the first three years of the survey (Y3A1). The FGCM combines data taken with auxiliary instrumentation at the observatory with data from the broad-band survey imaging itself and models of the instrument and atmosphere to estimate the spatial- and time-dependence of the passbands of individual DES survey exposures. "Standard" passbands are chosen that are typical of the passbands encountered during the survey. The passband of any individual observation is combined with an estimate of the source spectral shape to yield a magnitude $m_b^{\mathrm{std}}$ in the standard system. This "chromatic correction" to the standard system is necessary to achieve sub-percent calibrations. The FGCM achieves reproducible and stable photometric calibration of standard magnitudes $m_b^{\mathrm{std}}$ of stellar sources over the multi-year Y3A1 data sample with residual random calibration errors of $\sigma=5-6\,\mathrm{mmag}$ per exposure. The accuracy of the calibration is uniform across the $5000\,\mathrm{deg}^2$ DES footprint to within $\sigma=7\,\mathrm{mmag}$. The systematic uncertainties of magnitudes in the standard system due to the spectra of sources are less than $5\,\mathrm{mmag}$ for main sequence stars with $0.5<g-i<3.0$.Comment: 25 pages, submitted to A

Transfer learning for galaxy morphology from one survey to another

© 2018 The Author(s). Published by Oxford University Press on behalf of the Royal Astronomical Society.Deep Learning (DL) algorithms for morphological classification of galaxies have proven very successful, mimicking (or even improving) visual classifications. However, these algorithms rely on large training samples of labelled galaxies (typically thousands of them). A key question for using DL classifications in future Big Data surveys is how much of the knowledge acquired from an existing survey can be exported to a new dataset, i.e. if the features learned by the machines are meaningful for different data. We test the performance of DL models, trained with Sloan Digital Sky Survey (SDSS) data, on Dark Energy survey (DES) using images for a sample of $\sim$5000 galaxies with a similar redshift distribution to SDSS. Applying the models directly to DES data provides a reasonable global accuracy ($\sim$ 90%), but small completeness and purity values. A fast domain adaptation step, consisting in a further training with a small DES sample of galaxies ($\sim$500-300), is enough for obtaining an accuracy > 95% and a significant improvement in the completeness and purity values. This demonstrates that, once trained with a particular dataset, machines can quickly adapt to new instrument characteristics (e.g., PSF, seeing, depth), reducing by almost one order of magnitude the necessary training sample for morphological classification. Redshift evolution effects or significant depth differences are not taken into account in this study.Peer reviewedFinal Accepted Versio