1,662 research outputs found
Central Limit Theorems for some Set Partition Statistics
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
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
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
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
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
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
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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