Algebraic Bethe ansatz for the XXZ Heisenberg spin chain with triangular boundaries and the corresponding Gaudin model

The implementation of the algebraic Bethe ansatz for the XXZ Heisenberg spin chain, of arbitrary spin-$s$, in the case, when both reflection matrices have the upper-triangular form is analyzed. The general form of the Bethe vectors is studied. In the particular form, Bethe vectors admit the recurrent procedure, with an appropriate modification, used previously in the case of the XXX Heisenberg chain. As expected, these Bethe vectors yield the strikingly simple expression for the off-shell action of the transfer matrix of the chain as well as the spectrum of the transfer matrix and the corresponding Bethe equations. As in the XXX case, the so-called quasi-classical limit gives the off-shell action of the generating function of the corresponding trigonometric Gaudin Hamiltonians with boundary terms.Comment: 39 pages. Typos corrected. arXiv admin note: substantial text overlap with arXiv:1405.7398, arXiv:1412.139

sl_2 Gaudin model with Jordanian twist

sl_2 Gaudin model with Jordanian twist is studied. This system can be obtained as the semiclassical limit of the XXX spin chain deformed by the Jordanian twist. The appropriate creation operators that yield the Bethe states of the Gaudin model and consequently its spectrum are defined. Their commutation relations with the generators of the corresponding loop algebra as well as with the generating function of integrals of motion are given. The inner products and norms of Bethe states and the relation to the solutions of the Knizhnik-Zamolodchikov equations are discussed.Comment: 22 pages; corrected typo

Schlesinger transformations for elliptic isomonodromic deformations

Schlesinger transformations are discrete monodromy preserving symmetry transformations of the classical Schlesinger system. Generalizing well-known results from the Riemann sphere we construct these transformations for isomonodromic deformations on genus one Riemann surfaces. Their action on the system's tau-function is computed and we obtain an explicit expression for the ratio of the old and the transformed tau-function.Comment: 19 pages, LaTeX2

Generalized sℓ(2) Gaudin algebra and corresponding Knizhnik–Zamolodchikov equation

The Gaudin model has been revisited many times, yet some important issues remained open so far. With this paper we aim to properly address its certain aspects, while clarifying, or at least giving a solid ground to some other. Our main contribution is establishing the relation between the off-shell Bethe vectors with the solutions of the corresponding Knizhnik-Zamolodchikov equations for the non-periodic sl(2) Gaudin model, as well as deriving the norm of the eigenvectors of the Gaudin Hamiltonians. Additionally, we provide a closed form expression also for the scalar products of the off-shell Bethe vectors. Finally, we provide explicit closed form of the off-shell Bethe vectors, together with a proof of implementation of the algebraic Bethe ansatz in full generality. (C) 2019 The Authors.Foundation for Science and Technology (FCT), Portugal PTDC/MAT-GEO/3319/2014 Ministry of Education, Science and Technological Development, Serbia ON 171031info:eu-repo/semantics/publishedVersio

Algebraic Bethe Ansatz for deformed Gaudin model

The Gaudin model based on the sl_2-invariant r-matrix with an extra Jordanian term depending on the spectral parameters is considered. The appropriate creation operators defining the Bethe states of the system are constructed through a recurrence relation. The commutation relations between the generating function t(\lambda) of the integrals of motion and the creation operators are calculated and therefore the algebraic Bethe Ansatz is fully implemented. The energy spectrum as well as the corresponding Bethe equations of the system coincide with the ones of the sl_2-invariant Gaudin model. As opposed to the sl_2-invariant case, the operator t(\lambda) and the Gaudin Hamiltonians are not hermitian. Finally, the inner products and norms of the Bethe states are studied.Comment: 23 pages; presentation improve

Phytochemical, Antioxidant and Antimicrobial Profiles of Extracts of Daphne alpina (Thymelaeaceae) L Leaf and Twig from Mt Kopaonik (Serbia)

Purpose: To investigate the phytochemical composition, as well as antioxidant and antimicrobial activities of the leaf and twig extracts of Daphne alpina L. (Thymelaeaceae).Methods: The dry chloroform and methanol extracts of the leaf and twigs of Daphne alpinа were used for analysis. Total phenolic and flavonoid contents were determined by established procedures. Antioxidant potential was investigated by several methods. The antimicrobial properties of the extracts were obtained by microdilution method. High performance liquid chromatography (HPLC) was employed for the identification of the most abundant metabolites, present in D. alpina extracts.Results: The total phenolics of the extracts ranged from 78.98 to 88.98 mg GA/g while total flavonoids were in the range 28.09 to 34.65 mg GA/g of fresh weight. HPLC analysis of the extracts showed the presence 4-hydroxybenzoic acid, 7,8-dihydroxycoumarine and 7-hydroxycoumarine. Total antioxidant capacity ranged from 69.71 μg AA/g for the methanol leaf extract to 73.55 μg AA/g for the chloroform twig extract. All the extracts showed DPPH radical scavenging activity (21.57 - 25.45 μg/mL), inhibitory activity against lipid peroxidation (26.79 - 35.24 μg/mL), ferrous ion chelating ability (21.57 - 45.45 μg/ml) and hydroxyl radical scavenging activity (87.98 - 98.86 μg/mL). Minimum inhibitory concentration (MIC) was in the range 15.62 - 125 μg/mL.Conclusion: The extracts possess moderate antioxidant and antimicrobial activities due probably to the phenolic compounds in the extracts.Keywords: Daphne alpina, Coumarines, 4-Hydroxybenzoic Acid, Phenols, Flavonoids, Antimicrobial Activity, Antioxidant Activit