2,980 research outputs found
The triton in a finite volume
Understanding the volume dependence of the triton binding energy is an
important step towards lattice simulations of light nuclei. We calculate the
triton binding energy in a finite cubic box with periodic boundary conditions
to leading order in the pionless effective field theory. Higher order
corrections are estimated and the proper renormalization of our results is
verified explicitly. We present results for the physical triton as well as for
the pion-mass dependence of the triton spectrum near the ``critical'' pion
mass, Mpi_c ~ 197 MeV, where chiral effective field theory suggests that the
nucleon-nucleon scattering lengths in the singlet- and triplet-channels diverge
simultaneously. An extension of the Luescher formula to the three-body system
is implicit in our results.Comment: 11 pages, 4 figure
An Abundance of K3 Fibrations from Polyhedra with Interchangeable Parts
Even a cursory inspection of the Hodge plot associated with Calabi-Yau
threefolds that are hypersurfaces in toric varieties reveals striking
structures. These patterns correspond to webs of elliptic-K3 fibrations whose
mirror images are also elliptic-K3 fibrations. Such manifolds arise from
reflexive polytopes that can be cut into two parts along slices corresponding
to the K3 fibers. Any two half-polytopes over a given slice can be combined
into a reflexive polytope. This fact, together with a remarkable relation on
the additivity of Hodge numbers, explains much of the structure of the observed
patterns.Comment: 30 pages, 15 colour figure
Heterotic Models from Vector Bundles on Toric Calabi-Yau Manifolds
We systematically approach the construction of heterotic E_8 X E_8 Calabi-Yau
models, based on compact Calabi-Yau three-folds arising from toric geometry and
vector bundles on these manifolds. We focus on a simple class of 101 such
three-folds with smooth ambient spaces, on which we perform an exhaustive scan
and find all positive monad bundles with SU(N), N=3,4,5 structure groups,
subject to the heterotic anomaly cancellation constraint. We find that
anomaly-free positive monads exist on only 11 of these toric three-folds with a
total number of bundles of about 2000. Only 21 of these models, all of them on
three-folds realizable as hypersurfaces in products of projective spaces, allow
for three families of quarks and leptons. We also perform a preliminary scan
over the much larger class of semi-positive monads which leads to about 44000
bundles with 280 of them satisfying the three-family constraint. These 280
models provide a starting point for heterotic model building based on toric
three-folds.Comment: 41 pages, 5 figures. A table modified and a table adde
Three particles in a finite volume: The breakdown of spherical symmetry
Lattice simulations of light nuclei necessarily take place in finite volumes,
thus affecting their infrared properties. These effects can be addressed in a
model-independent manner using Effective Field Theories. We study the model
case of three identical bosons (mass m) with resonant two-body interactions in
a cubic box with periodic boundary conditions, which can also be generalized to
the three-nucleon system in a straightforward manner. Our results allow for the
removal of finite volume effects from lattice results as well as the
determination of infinite volume scattering parameters from the volume
dependence of the spectrum. We study the volume dependence of several states
below the break-up threshold, spanning one order of magnitude in the binding
energy in the infinite volume, for box side lengths L between the two-body
scattering length a and L = 0.25a. For example, a state with a three-body
energy of -3/(ma^2) in the infinite volume has been shifted to -10/(ma^2) at L
= a. Special emphasis is put on the consequences of the breakdown of spherical
symmetry and several ways to perturbatively treat the ensuing partial wave
admixtures. We find their contributions to be on the sub-percent level compared
to the strong volume dependence of the S-wave component. For shallow bound
states, we find a transition to boson-diboson scattering behavior when
decreasing the size of the finite volume.Comment: 21 pages, 4 figures, 2 table
Algebraic Topology of Calabi-Yau Threefolds in Toric Varieties
We compute the integral homology (including torsion), the topological
K-theory, and the Hodge structure on cohomology of Calabi-Yau threefold
hypersurfaces and complete intersections in Gorenstein toric Fano varieties.
The methods are purely topological
Influence of Cattle Stocking Rate on Browsing of Norway Spruce in Subalpine Wood Pastures
In the Swiss Alps, 15% of Swiss mountain forests are grazed during summer, mainly by cattle. The forest laws of various Swiss cantons characterise forest grazing as a detrimental form of land use and stipulate that this grazing practice should be restricted. However, little is known about tree damage actually caused by cattle. Seven subalpine ranges in the Swiss Canton Grisons, grazed by cattle at different stocking rates, were investigated. The condition of naturally regenerated young trees (Picea abies (L.) Karst.) was assessed before and after the cattle grazing period. In order to characterise the influence of wild ungulates on the young trees during winter, the assessment of tree condition was repeated in the proximate spring. In total, 4% of the young trees were browsed on the apical shoot, 10% were browsed on lateral shoots, 13% of the trees showed other damage. The variation among ranges could almost completely be explained by the cattle stocking rate (livestock units per hectare). During winter, wild ungulates browsed 3 times as many young trees as the cattle during summer. The results suggest that cattle stocking rates on subalpine wood pastures should not exceed one livestock unit per hectare in order to avoid intensive browsing and other damage by cattle on young Norway spruce
Homalg: A meta-package for homological algebra
The central notion of this work is that of a functor between categories of
finitely presented modules over so-called computable rings, i.e. rings R where
one can algorithmically solve inhomogeneous linear equations with coefficients
in R. The paper describes a way allowing one to realize such functors, e.g.
Hom, tensor product, Ext, Tor, as a mathematical object in a computer algebra
system. Once this is achieved, one can compose and derive functors and even
iterate this process without the need of any specific knowledge of these
functors. These ideas are realized in the ring independent package homalg. It
is designed to extend any computer algebra software implementing the
arithmetics of a computable ring R, as soon as the latter contains algorithms
to solve inhomogeneous linear equations with coefficients in R. Beside
explaining how this suffices, the paper describes the nature of the extensions
provided by homalg.Comment: clarified some points, added references and more interesting example
Toric Construction of Global F-Theory GUTs
We systematically construct a large number of compact Calabi-Yau fourfolds
which are suitable for F-theory model building. These elliptically fibered
Calabi-Yaus are complete intersections of two hypersurfaces in a six
dimensional ambient space. We first construct three-dimensional base manifolds
that are hypersurfaces in a toric ambient space. We search for divisors which
can support an F-theory GUT. The fourfolds are obtained as elliptic fibrations
over these base manifolds. We find that elementary conditions which are
motivated by F-theory GUTs lead to strong constraints on the geometry, which
significantly reduce the number of suitable models. The complete database of
models is available at http://hep.itp.tuwien.ac.at/f-theory/. We work out
several examples in more detail.Comment: 35 pages, references adde
A Modified Version of the Waxman Algorithm
The iterative algorithm recently proposed by Waxman for solving eigenvalue
problems, which relies on the method of moments, has been modified to improve
its convergence considerably without sacrificing its benefits or elegance. The
suggested modification is based on methods to calculate low-lying eigenpairs of
large bounded hermitian operators or matrices
The status of the quantum dissipation-fluctuation relation and Langevin equation
I examine the arguments which have been given for quantum
fluctuation-dissipation theorems. I distinguish between a weak form of the
theorem, which is true under rather general conditions, and a strong form which
requires a Langevin equation for its statement. I argue that the latter has not
been reliably derived.Comment: 9 page
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