Dynamics of vortex dipoles in anisotropic Bose-Einstein condensates

We study the motion of a vortex dipole in a Bose-Einstein condensate confined to an anisotropic trap. We focus on a system of ordinary differential equations describing the vortices' motion, which is in turn a reduced model of the Gross-Pitaevskii equation describing the condensate's motion. Using a sequence of canonical changes of variables, we reduce the dimension and simplify the equations of motion. We uncover two interesting regimes. Near a family of periodic orbits known as guiding centers, we find that the dynamics is essentially that of a pendulum coupled to a linear oscillator, leading to stochastic reversals in the overall direction of rotation of the dipole. Near the separatrix orbit in the isotropic system, we find other families of periodic, quasi-periodic, and chaotic trajectories. In a neighborhood of the guiding center orbits, we derive an explicit iterated map that simplifies the problem further. Numerical calculations are used to illustrate the phenomena discovered through the analysis. Using the results from the reduced system we are able to construct complex periodic orbits in the original, partial differential equation, mean-field model for Bose-Einstein condensates, which corroborates the phenomenology observed in the reduced dynamical equations

Parts of Quantum States

It is shown that generic N-party pure quantum states (with equidimensional subsystems) are uniquely determined by their reduced states of just over half the parties; in other words, all the information in almost all N-party pure states is in the set of reduced states of just over half the parties. For N even, the reduced states in fewer than N/2 parties are shown to be an insufficient description of almost all states (similar results hold when N is odd). It is noted that Real Algebraic Geometry is a natural framework for any analysis of parts of quantum states: two simple polynomials, a quadratic and a cubic, contain all of their structure. Algorithmic techniques are described which can provide conditions for sets of reduced states to belong to pure or mixed states.Comment: 10 pages, 1 figur

Neutrino masses, cosmological bound and four zero Yukawa textures

Four zero neutrino Yukawa textures in a specified weak basis, combined with $\mu\tau$ symmetry and type-I seesaw, yield a highly constrained and predictive scheme. Two alternately viable $3\times3$ light neutrino Majorana mass matrices $m_{\nu A}/m_{\nu B}$ result with inverted/normal mass ordering. Neutrino masses, Majorana in character and predicted within definite ranges with laboratory and cosmological inputs, will have their sum probed cosmologically. The rate for $0\nu\beta\beta$ decay, though generally below the reach of planned experiments, could approach it in some parameter region. Departure from $\mu\tau$ symmetry due to RG evolution from a high scale and consequent CP violation, with a Jarlskog invariant whose magnitude could almost reach $6\times 10^{-3}$, are explored.Comment: Published versio

The properties of the inner disk around HL Tau: Multi-wavelength modeling of the dust emission

We conducted a detailed radiative transfer modeling of the dust emission from the circumstellar disk around HL Tau. The goal of our study is to derive the surface density profile of the inner disk and its structure. In addition to the Atacama Large Millimeter/submillimeter Array images at Band 3 (2.9mm), Band 6 (1.3mm), and Band 7 (0.87mm), the most recent Karl G. Jansky Very Large Array (VLA) observations at 7mm were included in the analysis. A simulated annealing algorithm was invoked to search for the optimum model. The radiative transfer analysis demonstrates that most radial components (i.e., >6AU) of the disk become optically thin at a wavelength of 7mm, which allows us to constrain, for the first time, the dust density distribution in the inner region of the disk. We found that a homogeneous grain size distribution is not sufficient to explain the observed images at different wavelengths simultaneously, while models with a shallower grain size distribution in the inner disk work well. We found clear evidence that larger grains are trapped in the first bright ring. Our results imply that dust evolution has already taken place in the disk at a relatively young (i.e., ~1Myr) age. We compared the midplane temperature distribution, optical depth, and properties of various dust rings with those reported previously. Using the Toomre parameter, we briefly discussed the gravitational instability as a potential mechanism for the origin of the dust clump detected in the first bright ring via the VLA observations.Comment: Accepted for publication in A&A (10 pages

Limits on Associated Production of Visibly and Invisibly Decaying Higgs Bosons from Z Decays

Many extensions of the standard electroweak model Higgs sector suggest that the main Higgs decay channel is "invisible", for example, $h \to J J$ where $J$ denotes the majoron, a weakly interacting pseudoscalar Goldstone boson associated to the spontaneous violation of lepton number. In many of these models the Higgs boson may also be produced in association to a massive pseudoscalar boson (HA), in addition to the standard Bjorken mechanism (HZ). We describe a general strategy to determine limits from LEP data on the masses and couplings of such Higgs bosons, using the existing data on acoplanar dijet events as well as data on four and six $b$ jet event topologies. For the sake of illustration, we present constraints that can be obtained for the ALEPH data.Comment: FTUV/94-36, IFIC/94-31 TIFR/TH/94--25, 12 pages + 4 figures (included as ps files at the end

Integrating imaging-based classification and transcriptomics for quality assessment of human oocytes according to their reproductive efficiency

PURPOSE: Utilising non-invasive imaging parameters to assess human oocyte fertilisation, development and implantation; and their influence on transcriptomic profiles. METHODS: A ranking tool was designed using imaging data from 957 metaphase II stage oocytes retrieved from 102 patients undergoing ART. Hoffman modulation contrast microscopy was conducted with an Olympus IX53 microscope. Images were acquired prior to ICSI and processed using ImageJ for optical density and grey-level co-occurrence matrices texture analysis. Single-cell RNA sequencing of twenty-three mature oocytes classified according to their competence was performed. RESULT(S): Overall fertilisation, blastulation and implantation rates were 73.0%, 62.6% and 50.8%, respectively. Three different algorithms were produced using binary logistic regression methods based on "optimal" quartiles, resulting in an accuracy of prediction of 76.6%, 67% and 80.7% for fertilisation, blastulation and implantation. Optical density, gradient, inverse difference moment (homogeneity) and entropy (structural complexity) were the parameters with highest predictive properties. The ranking tool showed high sensitivity (68.9-90.8%) but with limited specificity (26.5-62.5%) for outcome prediction. Furthermore, five differentially expressed genes were identified when comparing "good" versus "poor" competent oocytes. CONCLUSION(S): Imaging properties can be used as a tool to assess differences in the ooplasm and predict laboratory and clinical outcomes. Transcriptomic analysis suggested that oocytes with lower competence may have compromised cell cycle either by non-reparable DNA damage or insufficient ooplasmic maturation. Further development of algorithms based on image parameters is encouraged, with an increased balanced cohort and validated prospectively in multicentric studies