119 research outputs found
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-, 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
- …