Covariance Properties of Reflection Equation Algebras

The reflection equations (RE) are a consistent extension of the Yang-Baxter equations (YBE) with an addition of one element, the so-called reflection matrix or $K$-matrix. For example, they describe the conditions for factorizable scattering on a half line just like the YBE give the conditions for factorizable scattering on an entire line. The YBE were generalized to define quadratic algebras, \lq Yang-Baxter algebras\rq\ (YBA), which were used intensively for the discussion of quantum groups. Similarly, the RE define quadratic algebras, \lq the reflection equation algebras\rq\ (REA), which enjoy various remarkable properties both new and inherited from the YBA. Here we focus on the various properties of the REA, in particular, the quantum group comodule properties, generation of a series of new solutions by composing known solutions, the extended REA and the central elements, etc.Comment: 31 pages, 8 figures (not included

Universal R-matrix as integral operator

We derive the integral operator form for the general rational solution of the Yang-Baxter equation with $s\ell(2|1)$ symmetry. Considering the defining relations for the kernel of the R-operator as a system of second order differential equations we observe remarkable reduction to a system of simple first order equations. The obtained kernel of R-operator has a very simple structure. To illustrate all this in the simplest situation we treat also the $s\ell(2)$ case.Comment: 26 pages LaTe

q-Supersymmetric Generalization of von Neumann's Theorem

Assuming that there exist operators which form an irreducible representation of the q-superoscillator algebra, it is proved that any two such representations are equivalent, related by a uniquely determined superunitary transformation. This provides with a q-supersymmetric generalization of the well-known uniqueness theorem of von Neumann for any finite number of degrees of freedom.Comment: 10 pages, Latex, HU-TFT-93-2

Heisenberg spin chains based on sl(2|1) symmetry

We find solutions of the Yang-Baxter equation acting on tensor product of arbitrary representations of the superalgebra sl(2|1). Based on these solutions we construct the local Hamiltonians for integrable homogeneous periodic chains and open chains.Comment: 28 pages LATE

Yang-Baxter R operators and parameter permutations

We present an uniform construction of the solution to the Yang- Baxter equation with the symmetry algebra $s\ell(2)$ and its deformations: the q-deformation and the elliptic deformation or Sklyanin algebra. The R-operator acting in the tensor product of two representations of the symmetry algebra with arbitrary spins $\ell_1$ and $\ell_2$ is built in terms of products of three basic operators $\mathcal{S}_1, \mathcal{S}_2,\mathcal{S}_3$ which are constructed explicitly. They have the simple meaning of representing elementary permutations of the symmetric group $\mathfrak{S}_4$, the permutation group of the four parameters entering the RLL-relation.Comment: 22 pages LaTex, comments added, version to be published in Nucl. Phys.

Universal R operator with Jordanian deformation of conformal symmetry

The Jordanian deformation of $sl(2)$ bi-algebra structure is studied in view of physical applications to breaking of conformal symmetry in the high energy asymptotics of scattering. Representations are formulated in terms of polynomials, generators in terms of differential operators. The deformed $R$ operator with generic representations is analyzed in spectral and integral forms.Comment: 25 pages LaTex, added reference

Quantum Matrix Models for Simple Current Orbifolds

An algebraic formulation of the stringy geometry on simple current orbifolds of the WZW models of type A_N is developed within the framework of Reflection Equation Algebras, REA_q(A_N). It is demonstrated that REA_q(A_N) has the same set of outer automorphisms as the corresponding current algebra A^{(1)}_N which is crucial for the orbifold construction. The CFT monodromy charge is naturally identified within the algebraic framework. The ensuing orbifold matrix models are shown to yield results on brane tensions and the algebra of functions in agreement with the exact BCFT data.Comment: 31 pages, LaTeX; typos corrected, new elements added, the contents restructure

Static and dynamic magnetic properties of K3CrO4

We report on the magnetic properties of geometrically frustrated K3CrO4, in which Cr5+ cations are arranged on a distorted pyrochlore lattice. The crystal structure, static and dynamic magnetic properties of the compound are investigated in detail. A combination of DC and AC magnetic susceptibility measurements together with thermoremanent magnetization decay measurements reveal several magnetic transitions: the onset of glassy canted antiferromagnetic order occurs at 36 K, followed by the appearance of ferromagnetic/ferrimagnetic cluster glass behavior below the freezing temperature of 20 K. Further field-induced, temperature-dependent transitions are observed in the range 3-10 K. The frequency dependence of the freezing temperature for the cluster glass state is analyzed on the basis of dynamic scaling laws including the critical slowing down formula and the Vogel-Fulcher law.Comment: A high-resolution version with supplementary material can be found at https://www.sciencedirect.com/science/article/pii/S0304885321004893?via%3Dihub. arXiv admin note: text overlap with arXiv:1912.0599

Selfconsistent Model of Photoconversion Efficiency for Multijunction Solar Cells

To accurately calculate efficiencies $\eta$ of experimentally produced multijunction solar cells (MJSCs) and optimize their parameters, we offer semi-analytical photoconversion formalism that incorporates radiative recombination, Shockley-Read-Hall (SRH) recombination, surface recombination at the front and back surfaces of the cells, recombination in the space charge region (SCR) and the recombination at the heterojunction boundaries. Selfconsistent balance between the MJSC temperature and efficiency was imposed by jointly solving the equations for the photocurrent, photovoltage, and heat balance. Finally, we incorporate into the formalism the effect of additional photocurrent decrease with subcell number increase. It is shown that for an experimentally observed Shockley-Read-Hall lifetimes, the effect of re-absorption and re-emission of photons on MJSC efficiency can be neglected for non-concentrated radiation conditions. A significant efficiency $\eta$ increase can be achieved by improving the heat dissipation using radiators and bringing the MJSC emissivity to unity, that is closer to black body radiation rather than grey body radiation. Our calculated efficiencies compare well with other numerical results available and are consistent with the experimentally achieved efficiencies. The formalism can be used to optimize parameters of MJSCs for maximum photoconversion efficiency.Comment: 40th IEEE Photovoltaic Specialists Conference, June 8-13, 2014, Denver, Colorado, III-V Epitaxy and Solar Cells, F30 16