Twisted quantum affine algebras and solutions to the Yang-Baxter equation

We construct spectral parameter dependent R-matrices for the quantized enveloping algebras of twisted affine Lie algebras. These give new solutions to the spectral parameter dependent quantum Yang-Baxter equation.Comment: Latex 24 pages. Misprints in eqs.(4.26) and (A.11) are corrected, cosmetic changes from "affine Kac-Moody algebras" to "affine Lie algebras" are made throughout the paper following a suggestion by M.B. Halpern, and one reference is adde

Solutions of the Yang-Baxter Equation with Extra Non-Additive Parameters II: Uq(gl(m∣n))U_q(gl(m|n))}

The type-I quantum superalgebras are known to admit non-trivial one-parameter families of inequivalent finite dimensional irreps, even for generic $q$. We apply the recently developed technique to construct new solutions to the quantum Yang-Baxter equation associated with the one-parameter family of irreps of $U_q(gl(m|n))$, thus obtaining R-matrices which depend not only on a spectral parameter but in addition on further continuous parameters. These extra parameters enter the Yang-Baxter equation in a similar way to the spectral parameter but in a non-additive form.Comment: 10 pages, LaTex file (some errors in the Casimirs corrected

On Type-I Quantum Affine Superalgebras

The type-I simple Lie-superalgebras are $sl(m|n)$ and $osp(2|2n)$. We study the quantum deformations of their untwisted affine extensions $U_q(sl(m|n)^{(1)})$ and $U_q(osp(2|2n)^{(1)})$. We identify additional relations between the simple generators (``extra $q$-Serre relations") which need to be imposed to properly define \uqgh and $U_q(osp(2|2n)^{(1)})$. We present a general technique for deriving the spectral parameter dependent R-matrices from quantum affine superalgebras. We determine the R-matrices for the type-I affine superalgebra $U_q(sl(m|n)^{(1)})$ in various representations, thereby deriving new solutions of the spectral-dependent Yang-Baxter equation. In particular, because this algebra possesses one-parameter families of finite-dimensional irreps, we are able to construct R-matrices depending on two additional spectral-like parameters, providing generalizations of the free-fermion model.Comment: 23 page

Infinite Families of Gauge-Equivalent RR-Matrices and Gradations of Quantized Affine Algebras

Associated with the fundamental representation of a quantum algebra such as $U_q(A_1)$ or $U_q(A_2)$, there exist infinitely many gauge-equivalent $R$-matrices with different spectral-parameter dependences. It is shown how these can be obtained by examining the infinitely many possible gradations of the corresponding quantum affine algebras, such as $U_q(A_1^{(1)})$ and $U_q(A_2^{(1)})$, and explicit formulae are obtained for those two cases. Spectral-dependent similarity (gauge) transformations relate the $R$-matrices in different gradations. Nevertheless, the choice of gradation can be physically significant, as is illustrated in the case of quantum affine Toda field theories.Comment: 14 pages, Latex, UQMATH-93-10 (final version for publication

The Electric Double Layer Structure Around Charged Spherical Interfaces

We derive a formally simple approximate analytical solution to the Poisson-Boltzmann equation for the spherical system via a geometric mapping. Its regime of applicability in the parameter space of the spherical radius and the surface potential is determined, and its superiority over the linearized solution is demonstrated.Comment: 7 pages, 5 figure

Quantum Lie algebras associated to Uq(gln)U_q(gl_n) and Uq(sln)U_q(sl_n)

Quantum Lie algebras \qlie{g} are non-associative algebras which are embedded into the quantized enveloping algebras $U_q(g)$ of Drinfeld and Jimbo in the same way as ordinary Lie algebras are embedded into their enveloping algebras. The quantum Lie product on \qlie{g} is induced by the quantum adjoint action of $U_q(g)$. We construct the quantum Lie algebras associated to $U_q(gl_n)$ and $U_q(sl_n)$. We determine the structure constants and the quantum root systems, which are now functions of the quantum parameter $q$. They exhibit an interesting duality symmetry under $q\leftrightarrow 1/q$.Comment: Latex 9 page

Uq[sl(2∣1)^]U_q[\hat{sl(2|1)}] Vertex Operators, Screen Currents and Correlation Functions at Arbitrary Level

Bosonized q-vertex operators related to the 4-dimensional evaluation modules of the quantum affine superalgebra $U_q[\hat{sl(2|1)}]$ are constructed for arbitrary level $k=\alpha$, where $\alpha\neq 0, -1$ is a complex parameter appearing in the 4-dimensional evaluation representations. They are intertwiners among the level-$\alpha$ highest weight Fock-Wakimoto modules. Screen currents which commute with the action of $U_q[\hat{sl(2|1)}]$ up to total differences are presented. Integral formulae for N-point functions of type I and type II q-vertex operators are proposed.Comment: Latex file 18 page

Electrical properties of Bi-implanted amorphous chalcogenide films

The impact of Bi implantation on the conductivity and the thermopower of amorphous chalcogenide films is investigated. Incorporation of Bi in Ge-Sb-Te and GeTe results in enhanced conductivity. The negative Seebeck coefficient confirms onset of the electron conductivity in GeTe implanted with Bi at a dose of 2x1016 cm-2. The enhanced conductivity is accompanied by defect accumulation in the films upon implantation as is inferred by using analysis of the space-charge limited current. The results indicate that native coordination defects in lone-pair semiconductors can be deactivated by means of ion implantation, and higher conductivity of the films stems from additional electrically active defects created by implantation of bismuth.Comment: This is an extended version of the results presented in Proc. SPIE 8982, 898213 (2014

Eight state supersymmetric UU model of strongly correlated fermions

An integrable eight state supersymmtric $U$ model is proposed, which is a fermion model with correlated single-particle and pair hoppings as well as uncorrelated triple-particle hopping. It has an $gl(3|1)$ supersymmetry and contains one symmetry-preserving free parameter. The model is solved and the Bethe ansatz equations are obtained.Comment: Some cosmetic changes; to appear in Phys. Rev.