98,310 research outputs found

    Bott-Chern blow-up formula and bimeromorphic invariance of the βˆ‚βˆ‚Λ‰\partial\bar{\partial}-Lemma for threefolds

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    The purpose of this paper is to study the bimeromorphic invariants of compact complex manifolds in terms of Bott-Chern cohomology. We prove a blow-up formula for Bott-Chern cohomology. As an application, we show that for compact complex threefolds the non-K\"{a}hlerness degrees, introduced by Angella-Tomassini [Invent. Math. 192, (2013), 71-81], are bimeromorphic invariants. Consequently, the βˆ‚βˆ‚Λ‰\partial\bar{\partial}-Lemma on threefolds admits the bimeromorphic invariance.Comment: 24 page

    Theoretical Details of Tunnel Magnetoresistance via inelastic hopping at regime gΞΌBβ‰ͺkBTβ‰ͺeVg\mu B\ll k_B T \ll eV

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    Detailed theoretical derivation is given for the tunnel magnetoresistance via phonon-assisted hopping through an impurity chain under small magnetic field and a large bias window. This derivation provides a rigorous basis for the physical picture of Pauli blockade switch proposed in our previous paper (arXiv:1404.0633). This picture captures the competition of external magnetic field and internal spin interactions in the tunnel barrier, and relies critically on the strong on-site Coulomb correlation at the impurities. The master equations are obtained by deriving the equations of motion for the Green functions at the impurity sites in a slave-boson representation, and utilizing the so-called Langreth theorem to finally express the spin-dependent density matrix in terms of the equilibrium distributions of the contact electrons and of the phonon reservoir.Comment: 13 pages, correct a typo in Eq.(14) and add an explanation for Eq.(19

    Dolbeault cohomologies of blowing up complex manifolds II: bundle-valued case

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    We use a sheaf-theoretic approach to obtain a blow-up formula for Dolbeault cohomology groups with values in the holomorphic vector bundle over a compact complex manifold. As applications, we present several positive (or negative) examples associated to the vanishing theorems of Girbau, Kawamata-Viehweg and Green-Lazarsfeld in a uniform manner and study the blow-up invariance of some classical holomorphic invariants.Comment: Final version with several typos fixed, to appear in Journal de Math\'ematiques Pures et Appliqu\'ees. 36 page

    Dolbeault cohomologies of blowing up complex manifolds

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    We prove a blow-up formula for Dolbeault cohomologies of compact complex manifolds by introducing relative Dolbeault cohomology. As corollaries, we present a uniform proof for bimeromorphic invariance of (βˆ™,0)(\bullet,0)- and (0,βˆ™)(0,\bullet)-Hodge numbers on a compact complex manifold, and obtain the equality for the numbers of the blow-ups and blow-downs in the weak factorization of the bimeromorphic map between two compact complex manifolds with equal (1,1)(1,1)-Hodge number or equivalently second Betti number. Many examples of the latter one are listed. Inspired by these, we obtain the bimeromorphic stability for degeneracy of the Fr\"olicher spectral sequences at E1E_1 on compact complex threefolds and fourfolds.Comment: All comments are welcome. 25 Page

    Polarization analysis of excitons in monolayer and bilayer transition-metal dichalcogenides

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    The polarization analysis of optical transitions in monolayer and bilayer transition-metal dichalcogenides provides invaluable information on the spin and valley (pseudospin) degrees of freedom. To explain optical properties of a given monolayer transition-metal dichalcogenide, one should consider (i) the order of its spin-split conduction bands, (ii) whether intervalley scattering is prone to phonon bottleneck, (iii) and whether valley mixing by electron-hole exchange can take place. Using these principles, we present a consistent physical picture that elucidates a variety of features in the optical spectra of these materials. We explain the differences between optical transitions in monolayer MoSe2_2 and monolayer WSe2_2, finding that indirect excitons in the latter correspond to several low-energy optical transitions that so far were attributed to excitons bound to impurities. A possible mechanism that can explain the vanishing polarization in MoSe2_2 is discussed. Finally, we consider the effect of an out-of-plane electric field, showing that it can reduce the initial polarization of bright excitons due to a Rashba-type coupling with dark excitons.Comment: we welcome any feedback (including missing references if prior to the official peer-reviewed publication

    An Etude on Recursion Relations and Triangulations

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    Following~\cite{Arkani-Hamed:2017thz}, we derive a recursion relation by applying a one-parameter deformation of kinematic variables for tree-level scattering amplitudes in bi-adjoint Ο•3\phi^3 theory. The recursion relies on properties of the amplitude that can be made manifest in the underlying kinematic associahedron, and it provides triangulations for the latter. Furthermore, we solve the recursion relation and present all-multiplicity results for the amplitude: by reformulating the associahedron in terms of its vertices, it is given explicitly as a sum of "volume" of simplicies for any triangulation, which is an analogy of BCFW representation/triangulation of amplituhedron for N=4{\cal N}=4 SYM.Comment: 26 pages, 3 figure

    S-index: Towards Better Metrics for Quantifying Research Impact

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    The ongoing growth in the volume of scientific literature available today precludes researchers from efficiently discerning the relevant from irrelevant content. Researchers are constantly interested in impactful papers, authors and venues in their respective fields. Moreover, they are interested in the so-called recent "rising stars" of these contexts which may lead to attractive directions for future work, collaborations or impactful publication venues. In this work, we address the problem of quantifying research impact in each of these contexts, in order to better direct attention of researchers and streamline the processes of comparison, ranking and evaluation of contribution. Specifically, we begin by outlining intuitive underlying assumptions that impact quantification methods should obey and evaluate when current state-of-the-art methods fail to satisfy these properties. To this end, we introduce the s-index metric which quantifies research impact through influence propagation over a heterogeneous citation network. s-index is tailored from these intuitive assumptions and offers a number of desirable qualities including robustness, natural temporality and straightforward extensibility from the paper impact to broader author and venue impact contexts. We evaluate its effectiveness on the publicly available Microsoft Academic Search citation graph with over 119 million papers and 1 billion citation edges with 103 million and 21 thousand associated authors and venues respectively

    Contextual Aware Joint Probability Model Towards Question Answering System

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    In this paper, we address the question answering challenge with the SQuAD 2.0 dataset. We design a model architecture which leverages BERT's capability of context-aware word embeddings and BiDAF's context interactive exploration mechanism. By integrating these two state-of-the-art architectures, our system tries to extract the contextual word representation at word and character levels, for better comprehension of both question and context and their correlations. We also propose our original joint posterior probability predictor module and its associated loss functions. Our best model so far obtains F1 score of 75.842% and EM score of 72.24% on the test PCE leaderboad

    Transport Theory of Monolayer Transition-Metal Dichalcogenides through Symmetry

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    We present a theory that elucidates the major momentum and spin relaxation processes for electrons, holes and hot excitons in monolayer transition-metal dichalcogenides. We expand on spin flips induced by flexural phonons and show that the spin relaxation is ultrafast for electrons in free-standing membranes while being mitigated in supported membranes. This behavior due to interaction with flexural phonons is universal in two-dimensional membranes that respect mirror symmetry and it leads to a counterintuitive inverse relation between mobility and spin relaxation.Comment: The published version. 5 pages main text is followed by 5 pages supplemental material

    Magnetic-Field-Modulated Resonant Tunneling in Ferromagnetic-Insulator-Nonmagnetic junctions

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    We present a theory for resonance-tunneling magnetoresistance (MR) in Ferromagnetic-Insulator-Nonmagnetic junctions. The theory sheds light on many of the recent electrical spin injection experiments, suggesting that this MR effect rather than spin accumulation in the nonmagnetic channel corresponds to the electrically detected signal. We quantify the dependence of the tunnel current on the magnetic field by quantum rate equations derived from the Anderson impurity model, with important addition of impurity spin interactions. Considering the on-site Coulomb correlation, the MR effect is caused by competition between the field, spin interactions and coupling to the magnetic lead. By extending the theory, we present a basis for operation of novel nm-size memories.Comment: 6 pages, 3 figures and 5-page supplemental material, bringing it closest to the published versio
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