Bethe ansatz for the XXX-S chain with non-diagonal open boundaries

We consider the algebraic Bethe ansatz solution of the integrable and isotropic XXX-S Heisenberg chain with non-diagonal open boundaries. We show that the corresponding K-matrices are similar to diagonal matrices with the help of suitable transformations independent of the spectral parameter. When the boundary parameters satisfy certain constraints we are able to formulate the diagonalization of the associated double-row transfer matrix by means of the quantum inverse scattering method. This allows us to derive explicit expressions for the eigenvalues and the corresponding Bethe ansatz equations. We also present evidences that the eigenvectors can be build up in terms of multiparticle states for arbitrary S.Comment: 62 page

The spectrum of an open vertex model based on the U_q[SU(2)] at roots of unity

We study the exact solution of an $N$-state vertex model based on the representation of the $U_q[SU(2)]$ algebra at roots of unity with diagonal open boundaries. We find that the respective reflection equation provides us one general class of diagonal $K$-matrices having one free-parameter. We determine the eigenvalues of the double-row transfer matrix and the respective Bethe ansatz equation within the algebraic Bethe ansatz framework. The structure of the Bethe ansatz equation combine a pseudomomenta function depending on a free-parameter with scattering phase-shifts that are fixed by the roots of unity and boundary variables.Comment: 21 page

The Bethe ansatz approach for factorizable centrally extended S-matrices

We consider the Bethe ansatz solution of integrable models interacting through factorized $S$-matrices based on the central extention of the $\bf{su}(2|2)$ symmetry. The respective $\bf{su}(2|2)$ $R$-matrix is explicitly related to that of the covering Hubbard model through a spectral parameter dependent transformation. This mapping allows us to diagonalize inhomogeneous transfer matrices whose statistical weights are given in terms of $\bf{su}(2|2)$ $S$-matrices by the algebraic Bethe ansatz. As a consequence of that we derive the quantization condition on the circle for the asymptotic momenta of particles scattering by the $\bf{su}(2|2) \otimes \bf{su}(2|2)$ $S$-matrix. The result for the quantization rule may be of relevance in the study of the energy spectrum of the $AdS_5 \times S^{5}$ string sigma model in the thermodynamic limit. \Comment: 22 pages, published versio

Al'Kalaeleth or The Account of The Creation of Aeleth

���Al���Kalaeleth; or The Account of the Creation of Aeleth��� is a mythopoeic creative thesis that is inspired by mythic literature, cognitive research, and philosophy, though it also has supporting inspiration from genre fantasy and poetry. It is the story of how an unnamed prophet goes up a mountain with his father, returning forty days later to give an account of the creation of the world to his followers. The Prophet���s account is a frame narrative from which the highly symbolic creation myth can be explained and elaborated upon. While The Prophet and his father reveal the long-hidden truth about existence to their followers, two cities plot against him, watching his words and tallying his sins. ���Al���Kalaeleth��� is one chapter of what will be developed into a greater novel. The frame narrative therefore allows philosophical questions of cognitive philosophy and phenomenology to be approached. There is also an underlying meta-narrative that focuses on the plot as occurring within an authorial mind. The work and its research are guided by the research question: In what ways do the antiquarian structures of myth reveal greater understandings of psychological realities through symbolic rhetoric, especially when looking at beliefs in things such as religion and societal values? However, the work also is guided by the following secondary research questions: How do mythic and fantasy literature use the symbolic when discussing the literal creation of the world and the metaphysical development of the human psyche? What insights can these belief structures give into the modern perception of the human mind, and in what ways have these ancient beliefs impacted the ways that modern society understands psychology and cognitive philosophy? ���Al���Kalaeleth��� does not answer these secondary questions as it does the primary one, instead, as a work of art, it is meant to enable the audience to explore these questions from angles that are not commonly explored in the modern day, while also serving as an entertaining work of mythopoeic fantasy literature. ���Al���Kalaeleth��� is an innovative work of literature, both experimental in nature and founded in the mythopoeic tradition that was first tread by greats such as J.R.R. Tolkien, Lord Dunsany, and William Blake. The work was first presented at the English Undergraduate Research Honors Symposium that occurred on March 27th of 2024. When the complete novel is eventually published, ���Al���Kalaeleth��� is likely to have changed. However, the core ideas presented within the work are foundational to the entire novel. Even if the story changes, this piece should not be disregarded as simply a working draft or memento but as a piece of art in its own right

Noninvasive system of transcranial magnetic stimulation focused and deep

Peer Reviewe

BB Intermeson Potentials in the Quark Model

In this paper we derive quark model results for scattering amplitudes and equivalent low energy potentials for heavy meson pairs, in which each meson contains a heavy quark. This "BB" system is an attractive theoretical laboratory for the study of the nuclear force between color singlets; the hadronic system is relatively simple, and there are lattice gauge theory (LGT) results for V_BB(r) which may be compared to phenomenological models. We find that the quark model potential (after lattice smearing) has qualitative similarities to the LGT potential in the two B*B* channels in which direct comparison is possible, although there is evidence of a difference in length scales. The quark model prediction of equal magnitude but opposite sign for I=0 and I=1 potentials also appears similar to LGT results at intermediate r. There may however be a discrepancy between the LGT and quark model I=1 BB potentials. A numerical study of the two-meson Schrodinger equations in the (bqbar)(bqbar) and (cqbar)(cqbar) sectors with the quark model potentials finds a single "molecule", in the I=0 BB* sector. Binding in other channels might occur if the quark model forces are augmented by pion exchange.Comment: 30 pages, 5 figures, revtex and epsfig. Submitted to Phys. Rev.

Scenario of Accelerating Universe from the Phenomenological \Lambda- Models

Dark matter, the major component of the matter content of the Universe, played a significant role at early stages during structure formation. But at present the Universe is dark energy dominated as well as accelerating. Here, the presence of dark energy has been established by including a time-dependent $\Lambda$ term in the Einstein's field equations. This model is compatible with the idea of an accelerating Universe so far as the value of the deceleration parameter is concerned. Possibility of a change in sign of the deceleration parameter is also discussed. The impact of considering the speed of light as variable in the field equations has also been investigated by using a well known time-dependent $\Lambda$ model.Comment: Latex, 9 pages, Major change

Partially filled stripes in the two dimensional Hubbard model: statics and dynamics

The internal structure of stripes in the two dimensional Hubbard model is studied by going beyond the Hartree-Fock approximation. Partially filled stripes, consistent with experimental observations, are stabilized by quantum fluctuations, included through the Configuration Interaction method. Hopping of short regions of the stripes in the transverse direction is comparable to the bare hopping element. The integrated value of $n_{\bf \vec{k}}$ compares well with experimental results.Comment: 4 page

BAs and boride III-V alloys

Boron arsenide, the typically-ignored member of the III-V arsenide series BAs-AlAs-GaAs-InAs is found to resemble silicon electronically: its Gamma conduction band minimum is p-like (Gamma_15), not s-like (Gamma_1c), it has an X_1c-like indirect band gap, and its bond charge is distributed almost equally on the two atoms in the unit cell, exhibiting nearly perfect covalency. The reasons for these are tracked down to the anomalously low atomic p orbital energy in the boron and to the unusually strong s-s repulsion in BAs relative to most other III-V compounds. We find unexpected valence band offsets of BAs with respect to GaAs and AlAs. The valence band maximum (VBM) of BAs is significantly higher than that of AlAs, despite the much smaller bond length of BAs, and the VBM of GaAs is only slightly higher than in BAs. These effects result from the unusually strong mixing of the cation and anion states at the VBM. For the BAs-GaAs alloys, we find (i) a relatively small (~3.5 eV) and composition-independent band gap bowing. This means that while addition of small amounts of nitrogen to GaAs lowers the gap, addition of small amounts of boron to GaAs raises the gap (ii) boron ``semi-localized'' states in the conduction band (similar to those in GaN-GaAs alloys), and (iii) bulk mixing enthalpies which are smaller than in GaN-GaAs alloys. The unique features of boride III-V alloys offer new opportunities in band gap engineering.Comment: 18 pages, 14 figures, 6 tables, 61 references. Accepted for publication in Phys. Rev. B. Scheduled to appear Oct. 15 200

Water quality on small ruminants’ dairy farms in Castelo Branco region

The importance of providing quality water for cleaning milking machines and other equipment is perhaps one of the most overlooked factors in ensuring milk quality on most dairy farms. Water for cleaning in the dairy barn is used for different situations, including for the process of milking, which requires cleaning and disinfection of the milking equipment, the milking parlour, and the milk cooling tank. Many factors on dairy farms can contribute to contamination of the raw milk, and one of the major factors responsible for this contamination is the water used to clean the milking and storage equipment.This work was financially supported by QRural Research Unit/IPCB and CERNAS-IPCB (UIDB/00681/2020, FCT).info:eu-repo/semantics/publishedVersio