41,972 research outputs found

    Bright solitons in asymmetrically trapped Bose-Einstein condensate

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    We study the dynamics of bright solitons in a Bose-Einstein condensate (BEC) confined in a highly asymmetric trap. While working within the f ramework of a variational approach we carry out the stability analysis o f BEC solitons against collapse. When the number of atoms in the soliton exceeds a critical number NcN_c, it undergoes the so called primary col lapse. We find an analytical expression for NcN_c in terms of appropriat e experimental quantities that are used to produce and confine the conde nsate. We further demonstrate that, in the geometry of the problem consi dered, the width of the soliton varies inversely as the number of consti tuent atoms.Comment: 5 pages, 1 figure

    Squeezed States and Hermite polynomials in a Complex Variable

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    Following the lines of the recent paper of J.-P. Gazeau and F. H. Szafraniec [J. Phys. A: Math. Theor. 44, 495201 (2011)], we construct here three types of coherent states, related to the Hermite polynomials in a complex variable which are orthogonal with respect to a non-rotationally invariant measure. We investigate relations between these coherent states and obtain the relationship between them and the squeezed states of quantum optics. We also obtain a second realization of the canonical coherent states in the Bargmann space of analytic functions, in terms of a squeezed basis. All this is done in the flavor of the classical approach of V. Bargmann [Commun. Pur. Appl. Math. 14, 187 (1961)].Comment: 15 page

    A Generative Model for Parts-based Object Segmentation

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    The Shape Boltzmann Machine (SBM) [1] has recently been introduced as a stateof-the-art model of foreground/background object shape. We extend the SBM to account for the foreground object’s parts. Our new model, the Multinomial SBM (MSBM), can capture both local and global statistics of part shapes accurately. We combine the MSBM with an appearance model to form a fully generative model of images of objects. Parts-based object segmentations are obtained simply by performing probabilistic inference in the model. We apply the model to two challenging datasets which exhibit significant shape and appearance variability, and find that it obtains results that are comparable to the state-of-the-art. There has been significant focus in computer vision on object recognition and detection e.g. [2], but a strong desire remains to obtain richer descriptions of objects than just their bounding boxes. One such description is a parts-based object segmentation, in which an image is partitioned into multiple sets of pixels, each belonging to either a part of the object of interest, or its background. The significance of parts in computer vision has been recognized since the earliest days of th

    A search for millimetric emission from Gamma Ray Bursts

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    We have used the 2- year Differential Microwave Radiometer data from the COsmic Background Explorer (COBE) satellite to systematically search for millimetric (31 - 90 GHz) emission from the Gamma Ray Bursts (GRBs) in the Burst And Transient Source Experiment (BATSE) GRB 3B catalog. The large beamsize of the COBE instrument (7 degs FWHM) allows for an efficient search of the large GRB positional error boxes, although it also means that fluxes from (point source) GRB objects will be somewhat diluted. A likelihood analysis has been used to look for a change in the level of millimetric emission from the locations of 81 GRB events during the first two years (1990 & 1991) of the COBE mission. The likelihood analysis determined that we did not find any significant millimetric signal before or after the occurance of the GRB. We find 95% confidence level upper limits of 175, 192 and 645 Jy or, in terms of fluxes, of 9.6, 16.3 and 54.8 10^{-13} erg/cm^2/s, respectively at 31, 53 and 90 GHz. We also look separately at different classes of GRBs, including a study of the top ten (in peak flux) GRBs, the "short burst" and "long burst" subsets, finding similar upper limits. While these limits may be somewhat higher than one would like, we estimate that using this technique with future planned missions could push these limits down to \sim 1 mJy.Comment: 21 pages, 5 figures, to be published in The Astrophysical Journa
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