1,662 research outputs found

    Central Limit Theorems for some Set Partition Statistics

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    We prove the conjectured limiting normality for the number of crossings of a uniformly chosen set partition of [n] = {1,2,...,n}. The arguments use a novel stochastic representation and are also used to prove central limit theorems for the dimension index and the number of levels

    Energy absorption by polymer crazing

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    During the past thirty years, a tremendous amount of research was done on the development of crazing in polymers. The phenomenon of crazing was recognized as an unusual deformation behavior associated with a process of molecular orientation in a solid to resist failure. The craze absorbs a fairly large amount of energy during the crazing process. When a craze does occur the surrounding bulk material is usually stretched to several hundred percent of its original dimension and creates a new phase. The total energy absorbed by a craze during the crazing process in creep was calculated analytically with the help of some experimental measurements. A comparison of the energy absorption by the new phase and that by the original bulk uncrazed medium is made

    Pancharatnam and Berry Phases in Three-Level Photonic Systems

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    A theoretical analysis of Pancharatnam and Berry phases is made for biphoton three-level systems, which are produced via frequency degenerate co-linear spontaneous parametric down conversion (SPDC). The general theory of Pancharatnam phases is discussed with a special emphasis on geodesic 'curves'in Hilbert space. Explicit expressions for Pancharatnam, dynamical and geometrical phases are derived for the transformations produced by linear phase-converters. The problem of gauge invariance is treated along all the article

    Novel magnetic orderings in the kagome Kondo-lattice model

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    We consider the Kondo-lattice model on the kagome lattice and study its weak-coupling instabilities at band filling fractions for which the Fermi surface has singularities. These singularites include Dirac points, quadratic Fermi points in contact with a flat band, and Van Hove saddle points. By combining a controlled analytical approach with large-scale numerical simulations, we demonstrate that the weak-coupling instabilities of the Kondo-lattice model lead to exotic magnetic orderings. In particular, some of these magnetic orderings produce a spontaneous quantum anomalous Hall state.Comment: 15 pages, 11 figure

    The structure of Gelfand-Levitan-Marchenko type equations for Delsarte transmutation operators of linear multi-dimensional differential operators and operator pencils. Part 1

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    An analog of Gelfand-Levitan-Marchenko integral equations for multi- dimensional Delsarte transmutation operators is constructed by means of studying their differential-geometric structure based on the classical Lagrange identity for a formally conjugated pair of differential operators. An extension of the method for the case of affine pencils of differential operators is suggested.Comment: 12 page

    Broken parity and a chiral ground state in the frustrated magnet CdCr2O4

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    We present a model describing the lattice distortion and incommensurate magnetic order in the spinel CdCr2O4, a good realization of the Heisenberg "pyrochlore" antiferromagnet. The magnetic frustration is relieved through the spin-Peierls distortion of the lattice involving a phonon doublet with odd parity. The distortion stablizes a collinear magnetic order with the propagation wavevector q=2\pi(0,0,1). The lack of inversion symmetry makes the crystal structure chiral. The handedness is transferred to magnetic order by the relativistic spin-orbit coupling: the collinear state is twisted into a long spiral with the spins in the ac plane and q shifted to 2\pi(0,\delta,1).Comment: Incremental changes in response to referee report

    Torsion induces Gravity

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    In this work the Poincare-Chern Simons and Anti de Sitter Chern Simons gravities are studied. For both a solution that can be casted as a black hole with manifest torsion is found. Those solutions resemble Schwarzschild and Schwarzschild-AdS solutions respectively.Comment: 4 pages, RevTe
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