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

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

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 $(\tau)$-representation. Away from the critical momentum $p=\pi$ finite size effects turn out to be small except for the large $\tau$ limit. The large finite size effects at the critical momentum $p=\pi$ signal the emergence of infrared singularities in the spectral $(\omega)$-representation of the dynamical structure factors.Comment: PostScript file with 12 pages + 11 figures uuencoded compresse

XXZ Bethe states as highest weight vectors of the sl2sl_2 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 $sl_2$ loop algebra, for some restricted sectors with respect to eigenvalues of the total spin operator $S^Z$, 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

Auxiliary matrices on both sides of the equator

The spectra of previously constructed auxiliary matrices for the six-vertex model at roots of unity are investigated for spin-chains of even and odd length. The two cases show remarkable differences. In particular, it is shown that for even roots of unity and an odd number of sites the eigenvalues contain two linear independent solutions to Baxter's TQ-equation corresponding to the Bethe ansatz equations above and below the equator. In contrast, one finds for even spin-chains only one linear independent solution and complete strings. The other main result is the proof of a previous conjecture on the degeneracies of the six-vertex model at roots of unity. The proof rests on the derivation of a functional equation for the auxiliary matrices which is closely related to a functional equation for the eight-vertex model conjectured by Fabricius and McCoy.Comment: 22 pages; 2nd version: one paragraph added in the conclusion and some typos correcte

The Q-operator for Root-of-Unity Symmetry in Six Vertex Model

We construct the explicit $Q$-operator incorporated with the $sl_2$-loop-algebra symmetry of the six-vertex model at roots of unity. The functional relations involving the $Q$-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 $N$-state chiral Potts model. We show that the whole set of functional equations is valid for the $Q$-operator. Direct calculations in certain cases are also given here for clearer illustration about the nature of the $Q$-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

Critical Behavior of an Ising System on the Sierpinski Carpet: A Short-Time Dynamics Study

The short-time dynamic evolution of an Ising model embedded in an infinitely ramified fractal structure with noninteger Hausdorff dimension was studied using Monte Carlo simulations. Completely ordered and disordered spin configurations were used as initial states for the dynamic simulations. In both cases, the evolution of the physical observables follows a power-law behavior. Based on this fact, the complete set of critical exponents characteristic of a second-order phase transition was evaluated. Also, the dynamic exponent $\theta$ of the critical initial increase in magnetization, as well as the critical temperature, were computed. The exponent $\theta$ exhibits a weak dependence on the initial (small) magnetization. On the other hand, the dynamic exponent $z$ shows a systematic decrease when the segmentation step is increased, i.e., when the system size becomes larger. Our results suggest that the effective noninteger dimension for the second-order phase transition is noticeably smaller than the Hausdorff dimension. Even when the behavior of the magnetization (in the case of the ordered initial state) and the autocorrelation (in the case of the disordered initial state) with time are very well fitted by power laws, the precision of our simulations allows us to detect the presence of a soft oscillation of the same type in both magnitudes that we attribute to the topological details of the generating cell at any scale.Comment: 10 figures, 4 tables and 14 page

Lineshape predictions via Bethe ansatz for the one-dimensional spin-1/2 Heisenberg antiferromagnet in a magnetic field

The spin fluctuations parallel to the external magnetic field in the ground state of the one-dimensional (1D) s=1/2 Heisenberg antiferromagnet are dominated by a two-parameter set of collective excitations. In a cyclic chain of N sites and magnetization 0<M_z<N/2, the ground state, which contains 2M_z spinons, is reconfigured as the physical vacuum for a different species of quasi-particles, identifiable in the framework of the coordinate Bethe ansatz by characteristic configurations of Bethe quantum numbers. The dynamically dominant excitations are found to be scattering states of two such quasi-particles. For N -> \infty, these collective excitations form a continuum in (q,\omega)-space with an incommensurate soft mode. Their matrix elements in the dynamic spin structure factor S_{zz}(q,\omega) are calculated directly from the Bethe wave functions for finite N. The resulting lineshape predictions for N -> \infty complement the exact results previously derived via algebraic analysis for the exact 2-spinon part of S_{zz}(q,\omega) in the zero-field limit. They are directly relevant for the interpretation of neutron scattering data measured in nonzero field on quasi-1D antiferromagnetic compounds.Comment: 10 page

Auxiliary matrices for the six-vertex model and the algebraic Bethe ansatz

We connect two alternative concepts of solving integrable models, Baxter's method of auxiliary matrices (or Q-operators) and the algebraic Bethe ansatz. The main steps of the calculation are performed in a general setting and a formula for the Bethe eigenvalues of the Q-operator is derived. A proof is given for states which contain up to three Bethe roots. Further evidence is provided by relating the findings to the six-vertex fusion hierarchy. For the XXZ spin-chain we analyze the cases when the deformation parameter of the underlying quantum group is evaluated both at and away from a root of unity.Comment: 32 page

Theory of Pump Depletion and Spike Formation in Stimulated Raman Scattering

By using the inverse spectral transform, the SRS equations are solved and the explicit output data is given for arbitrary laser pump and Stokes seed profiles injected on a vacuum of optical phonons. For long duration laser pulses, this solution is modified such as to take into account the damping rate of the optical phonon wave. This model is used to interprete the experiments of Druhl, Wenzel and Carlsten (Phys. Rev. Lett., (1983) vol. 51, p. 1171), in particular the creation of a spike of (anomalous) pump radiation. The related nonlinear Fourier spectrum does not contain discrete eigenvalue, hence this Raman spike is not a soliton.Comment: LaTex file, includes two figures in LaTex format, 9 page