2,515 research outputs found
A new Q-matrix in the Eight-Vertex Model
We construct a -matrix for the eight-vertex model at roots of unity for
crossing parameter with odd , a case for which the existing
constructions do not work. The new -matrix \Q depends as usual on the
spectral parameter and also on a free parameter . For \Q has the
standard properties. For , however, it does not commute with the
operator and not with itself for different values of the spectral
parameter. We show that the six-vertex limit of \Q(v,t=iK'/2) exists.Comment: 10 pages section on quasiperiodicity added, typo corrected, published
versio
The Q-operator and Functional Relations of the Eight-vertex Model at Root-of-unity for odd N
Following Baxter's method of producing Q_{72}-operator, we construct the
Q-operator of the root-of-unity eight-vertex model for the crossing parameter
with odd where Q_{72} does not exist. We use this
new Q-operator to study the functional relations in the Fabricius-McCoy
comparison between the root-of-unity eight-vertex model and the superintegrable
N-state chiral Potts model. By the compatibility of the constructed Q-operator
with the structure of Baxter's eight-vertex (solid-on-solid) SOS model, we
verify the set of functional relations of the root-of-unity eight-vertex model
using the explicit form of the Q-operator and fusion weights of SOS model.Comment: Latex 28 page; Typos corrected, minor changes in presentation,
References added and updated-Journal versio
COMPLETE SOLUTION OF THE XXZ-MODEL ON FINITE RINGS. DYNAMICAL STRUCTURE FACTORS AT ZERO TEMPERATURE.
The finite size effects of the dynamical structure factors in the XXZ-model
are studied in the euclidean time -representation. Away from the
critical momentum finite size effects turn out to be small except for
the large limit. The large finite size effects at the critical momentum
signal the emergence of infrared singularities in the spectral
-representation of the dynamical structure factors.Comment: PostScript file with 12 pages + 11 figures uuencoded compresse
Selecting medicinal plants for cultivation at Nqabara on the Eastern Cape Wild Coast, South Africa
[From introduction:] The intensive harvesting of medicinal plants for commercial trade in South Africa poses a threat to many species. Cultivation has therefore been considered as an alternative to collection in the wild. This paper aims to assess the feasibility of cultivating medicinal plants in the Nqabara Administrative Area on South Africa's Wild Coast. A combination of participatory and formal research methods was used to collect data on the importance of medicinal plants, collection localities, market prices, the time spent collecting plants and their ease of cultivation. The values attached to medicinal plants were mainly dependent on their market prices. Four of the five Nqabara traditional healers interviewed cultivated these plants in their home gardens, but many medicinal products were obtained in indigenous forests from the bark of large trees, which were unsuitable for cultivation. Collectors said that the proximity of forests to their homesteads and the richness of forests in medicinal plants influenced their selection of harvesting localities. There was no correlation between time spent collecting species and their market prices. These prices were, however, positively correlated with the species' perceived healing properties. Users acknowledged that harvesting had an adverse effect on large trees, are eager to cultivate them and are taking action to conserve indigenous forests. Community-based enterprises should focus on species that are easy to cultivate and have a high demand, such as Stangeria eriopus, Acalypha glabrata and Behnia reticulata but not Araujia sericifera, which is exotic and abundant. The main barriers to commercial cultivation are availability of suitable land, water, lack of start-up capital, and access to markets and to seeds. Cultivation of medicinal plants could contribute to the economic empowerment of women in rural areas
The Dynamical Fingerprint of Core Scouring in Massive Elliptical Galaxies
The most massive elliptical galaxies have low-density centers or cores that
differ dramatically from the high-density centers of less massive ellipticals
and bulges of disk galaxies. These cores have been interpreted as the result of
mergers of supermassive black hole binaries, which depopulate galaxy centers by
gravitationally slingshotting central stars toward large radii. Such binaries
naturally form in mergers of luminous galaxies. Here, we analyze the population
of central stellar orbits in 11 massive elliptical galaxies that we observed
with the integral field spectrograph SINFONI at the European Southern
Observatory Very Large Telescope. Our dynamical analysis is orbit-based and
includes the effects of a central black hole, the mass distribution of the
stars, and a dark matter halo. We show that the use of integral field
kinematics and the inclusion of dark matter is important to conclude upon the
distribution of stellar orbits in galaxy centers. Six of our galaxies are core
galaxies. In these six galaxies, but not in the galaxies without cores, we
detect a coherent lack of stars on radial orbits in the core region and a
uniform excess of radial orbits outside of it: when scaled by the core radius,
the radial profiles of the classical anisotropy parameter beta are nearly
identical in core galaxies. Moreover, they match quantitatively the predictions
of black hole binary simulations, providing the first convincing dynamical
evidence for core scouring in the most massive elliptical galaxies.Comment: 8 pages, 3 figures, accepted by Ap
The Q-operator for Root-of-Unity Symmetry in Six Vertex Model
We construct the explicit -operator incorporated with the
-loop-algebra symmetry of the six-vertex model at roots of unity. The
functional relations involving the -operator, the six-vertex transfer matrix
and fusion matrices are derived from the Bethe equation, parallel to the
Onsager-algebra-symmetry discussion in the superintegrable -state chiral
Potts model. We show that the whole set of functional equations is valid for
the -operator. Direct calculations in certain cases are also given here for
clearer illustration about the nature of the -operator in the symmetry study
of root-of-unity six-vertex model from the functional-relation aspect.Comment: Latex 26 Pages; Typos and small errors corrected, Some explanations
added for clearer presentation, References updated-Journal version with
modified labelling of sections and formula
XXZ Bethe states as highest weight vectors of the loop algebra at roots of unity
We show that every regular Bethe ansatz eigenvector of the XXZ spin chain at
roots of unity is a highest weight vector of the loop algebra, for some
restricted sectors with respect to eigenvalues of the total spin operator
, and evaluate explicitly the highest weight in terms of the Bethe roots.
We also discuss whether a given regular Bethe state in the sectors generates an
irreducible representation or not. In fact, we present such a regular Bethe
state in the inhomogeneous case that generates a reducible Weyl module. Here,
we call a solution of the Bethe ansatz equations which is given by a set of
distinct and finite rapidities {\it regular Bethe roots}. We call a nonzero
Bethe ansatz eigenvector with regular Bethe roots a {\it regular Bethe state}.Comment: 40pages; revised versio
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Measuring Dark Matter Profiles Non-Parametrically In Dwarf Spheroidals: An Application To Draco
We introduce a novel implementation of orbit-based (or Schwarzschild) modeling that allows dark matter density profiles to be calculated non-parametrically in nearby galaxies. Our models require no assumptions to be made about velocity anisotropy or the dark matter profile. The technique can be applied to any dispersion-supported stellar system, and we demonstrate its use by studying the Local Group dwarf spheroidal galaxy (dSph) Draco. We use existing kinematic data at larger radii and also present 12 new radial velocities within the central 13 pc obtained with the VIRUS-W integral field spectrograph on the 2.7 m telescope at McDonald Observatory. Our non-parametric Schwarzschild models find strong evidence that the dark matter profile in Draco is cuspy for 20 = 20 pc is well fit by a power law with slope alpha = -1.0 +/- 0.2, consistent with predictions from cold dark matter simulations. Our models confirm that, despite its low baryon content relative to other dSphs, Draco lives in a massive halo.NSF-0908639Astronom
Temperature dependent spatial oscillations in the correlations of the XXZ spin chain
We study the correlation for the XXZ chain in the
massless attractive (ferromagnetic) region at positive temperatures by means of
a numerical study of the quantum transfer matrix. We find that there is a range
of temperature where the behavior of the correlation for large separations is
oscillatory with an incommensurate period which depends on temperature.Comment: 4 pages, REVTEX, 6 table
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