4,027 research outputs found

    Generalized Ehrhart polynomials

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    Let PP be a polytope with rational vertices. A classical theorem of Ehrhart states that the number of lattice points in the dilations P(n)=nPP(n) = nP is a quasi-polynomial in nn. We generalize this theorem by allowing the vertices of P(n) to be arbitrary rational functions in nn. In this case we prove that the number of lattice points in P(n) is a quasi-polynomial for nn sufficiently large. Our work was motivated by a conjecture of Ehrhart on the number of solutions to parametrized linear Diophantine equations whose coefficients are polynomials in nn, and we explain how these two problems are related.Comment: 18 pages, no figures; v2: Sections 4 and 5 added, proofs and exposition have been expanded and clarifie

    Magnetoresistance from Fermi Surface Topology

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    Extremely large non-saturating magnetoresistance has recently been reported for a large number of both topologically trivial and non-trivial materials. Different mechanisms have been proposed to explain the observed magnetotransport properties, yet without arriving to definitive conclusions or portraying a global picture. In this work, we investigate the transverse magnetoresistance of materials by combining the Fermi surfaces calculated from first principles with the Boltzmann transport theory approach relying on the semiclassical model and the relaxation time approximation. We first consider a series of simple model Fermi surfaces to provide a didactic introduction into the charge-carrier compensation and open-orbit mechanisms leading to non-saturating magnetoresistance. We then address in detail magnetotransport in three representative materials: (i) copper, a prototypical nearly free-electron metal characterized by the open Fermi surface that results in an intricate angular magnetoresistance, (ii) bismuth, a topologically trivial semimetal in which very large magnetoresistance is known to result from charge-carrier compensation, and (iii) tungsten diphosphide WP2, a recently discovered type-II Weyl semimetal that holds the record of magnetoresistance in compounds. In all three cases our calculations show excellent agreement with both the field dependence of magnetoresistance and its anisotropy measured at low temperatures. Furthermore, the calculations allow for a full interpretation of the observed features in terms of the Fermi surface topology. These results will help addressing a number of outstanding questions, such as the role of the topological phase in the pronounced large non-saturating magnetoresistance observed in topological materials.Comment: 13 pages, 9 figure

    CPCP violation in charmed hadron decays into neutral kaons

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    We find a new CPCP violating effect in charmed hadron decays into neutral kaons, which is induced by the interference between the Cabibbo-favored and doubly Cabibbo-suppressed amplitudes with the K0−K‾0K^{0}-\overline K^{0} mixing. It is estimated to be of order of O(10−3)\mathcal{O}(10^{-3}), much larger than the direct CPCP asymmetry, but missed in the literature. To reveal this new CPCP violation effect, we propose a new observable, the difference of the CPCP asymmetries in the D+→π+KS0D^{+}\to \pi^{+}K_S^0 and Ds+→K+KS0D_{s}^{+}\to K^{+} K_S^0 modes. Once the new effect is determined by experiments, the direct CPCP asymmetry then can be extracted and used to search for new physics.Comment: 6 pages, 3 figures. Contribution to the proceeding of The 15th International Conference on Flavor Physics & CP Violation, 5-9 June 2017, Prague, Czech Republi
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