12,413 research outputs found

    Properties of the one-dimensional Bose-Hubbard model from a high-order perturbative expansion

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    We employ a high-order perturbative expansion to characterize the ground state of the Mott phase of the one-dimensional Bose-Hubbard model. We compute for different integer filling factors the energy per lattice site, the two-point and density-density correlations, and expectation values of powers of the on-site number operator determining the local atom number fluctuations (variance, skewness, kurtosis). We compare these expansions to numerical simulations of the infinite-size system to determine their range of applicability. We also discuss a new sum rule for the density-density correlations that can be used in both equilibrium and non-equilibrium systems.Comment: 16 pages, published versio

    Beryllium Enhancement as Evidence for Accretion in a Lithium-Rich F Dwarf

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    The early F dwarf star ``J37'' in the open cluster NGC6633 shows an unusual pattern of photospheric abundances, including an order of magnitude enhancement of lithium and iron-peak elements, but an under-abundance of carbon. As a consequence of its thin convection zone these anomalies have been attributed to either radiative diffusion or the accretion of hydrogen-depleted material. By comparing high resolution VLT/UVES spectra of J37 (and other F stars in NGC 6633) with syntheses of the Be ii doublet region at 3131 Ang, we establish that J37 also has a Be abundance (A(Be)=3.0+/-0.5) that is at least ten times the cosmic value. This contradicts radiative diffusion models that produce a Li over-abundance, as they also predict photospheric Be depletion. Instead, since Be is a highly refractory element, it supports the notion that J37 is the first clear example of a star that has accreted volatile-depleted material with a composition similar to chondritic meteorites, although some diffusion may be necessary to explain the low C and O abundances.Comment: Accepted for publication in MNRAS letters, 5 page

    Studies of Stellar Collapse and Black Hole Formation with the Open-Source Code GR1D

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    We discuss results from simulations of black hole formation in failing core-collapse supernovae performed with the code GR1D, a new open-source Eulerian spherically-symmetric general-relativistic hydrodynamics code. GR1D includes rotation in an approximate way (1.5D) comes with multiple finite-temperature nuclear equations of state (EOS), and treats neutrinos in the post-core-bounce phase via a 3-flavor leakage scheme and a heating prescription. We chose the favored K_0 = 220 MeV-variant of the Lattimer & Swesty (1990) EOS and present collapse calculations using the progenitor models of Limongi & Chieffi (2006). We show that there is no direct (or “prompt”) black hole formation in the collapse of ordinary massive stars (8M_☉ ≲ M_(ZAMS) ≲ 100 M_☉) present first results from black hole formation simulations that include rotation

    The invariants of the binary nonic

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    We consider the algebra of invariants of binary forms of degree 9 with complex coefficients, find the 92 basic invariants, give an explicit system of parameters and show the existence of four more systems of parameters with different sets of degrees
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