Tetrahedron Equation and Quantum R Matrices for Spin Representations of {B^{(1)}_n}, {D^{(1)}_n} and {D^{(2)}_{n+1}}

It is known that a solution of the tetrahedron equation generates infinitely many solutions of the Yang-Baxter equation via suitable reductions. In this paper this scheme is applied to an oscillator solution of the tetrahedron equation involving bosons and fermions by using special 3d boundary conditions. The resulting solutions of the Yang-Baxter equation are identified with the quantum R matrices for the spin representations of ${B^{(1)}_n}$ , ${D^{(1)}_n}$ and ${D^{(2)}_{n+1}}$ .     

Cluster model of defective solid solutionsMe_{c_1 }^{(1)} Me_{c_2 }^{(2)} B_x^{(1)} B_y^{(2)}

In a cluster model of defective solid solutions the cluster components are determined and their concentration is found as a function of the defectiveness for solutions \(Me_{c_1 }^{(1)} Me_{c_2 }^{(2)} B_x^{(1)} B_y^{(2)}\) in the case of limited and unlimited solubility. An interpretation is given of the dependence of the lattice parameter, magnetic moment, and Curie point on the composition in a cluster component model, using the example of oxycarbides, oxynitrides, and solutions of certain metals in Mn₄N.     

Compound Basis Arising from the Basic {A^{(1)}_{1}}-Module

Given a conditionally completely positive map on a unital *-algebra , we find an interesting connection between the second Hochschild cohomology of with coefficients in the bimodule of adjointable maps, where M is the GNS bimodule of , and the possibility of constructing a quantum random walk [in the sense of (Attal et al. in Ann Henri Poincar 7(1):59–104, 2006; Lindsay and Parthasarathy in Sankhya Ser A 50(2):151–170, 1988; Sahu in Quantum stochastic Dilation of a class of Quantum dynamical Semigroups and Quantum random walks. Indian Statistical Institute, 2005; Sinha in Banach Center Publ 73:377–390, 2006)] corresponding to . D. Goswami was supported by a project funded by the Indian National Academy of Sciences. L. Sahu had research support from the National Board of Higher Mathematics, DAE (India) is gratefully acknowledged.     

A q-boson representation of Zamolodchikov-Faddeev algebra for stochastic R matrix of $$\varvec{U_ q(A^{(1)}_n)}$$U q(An(1))

We construct a q-boson representation of the Zamolodchikov-Faddeev algebra whose structure function is given by the stochastic R matrix of \(U_q(A^{(1)}_n)\) introduced recently. The representation involves quantum dilogarithm type infinite products in the \(n(n-1)/2\)-fold tensor product of q-bosons. It leads to a matrix product formula of the stationary probabilities in the \(U_q(A_n^{(1)})\)-zero range process on a one-dimensional periodic lattice.     

Stability of {\text{SrCe}}_{{0.9}} {\text{Eu}}_{{0.1}} {\text{O}}_{{3 - \delta }} and {\text{SrZr}}_{{0.2}} {\text{Ce}}_{{0.7}} {\text{Eu}}_{{0.1}} {\text{O}}_{{3 - \delta }} under H2 atmospheres

Previous H₂ permeation tests showed a degradation of H₂ permeation flux with time. To understand the cause of degradation and develop a solution, the stability of $ {\text{SrCe}}_{{0.9}} {\text{Eu}}_{{0.1}} {\text{O}}_{{3 - \delta }} $ and $ {\text{SrZr}}_{{0.2}} {\text{Ce}}_{{0.7}} {\text{Eu}}_{{0.1}} {\text{O}}_{{3 - \delta }} $ samples were studied under dry and wet H₂ atmospheres. Total conductivity of $ {\text{SrCe}}_{{0.9}} {\text{Eu}}_{{0.1}} {\text{O}}_{{3 - \delta }} $ increased with time in dry H₂. The X-ray diffraction pattern of $ {\text{SrCe}}_{{0.9}} {\text{Eu}}_{{0.1}} {\text{O}}_{{3 - \delta }} $ after dry hydrogen atmosphere heat treatments show CeO₂ peaks indicating that $ {\text{SrCe}}_{{0.9}} {\text{Eu}}_{{0.1}} {\text{O}}_{{3 - \delta }} $ decomposes under dry H₂ atmospheres; scanning electron microscopy and energy dispersive X-ray spectroscopy analyses prove that decomposition proceeded along the grain boundaries. $ {\text{SrZr}}_{{0.2}} {\text{Ce}}_{{0.7}} {\text{Eu}}_{{0.1}} {\text{O}}_{{3 - \delta }} $ was investigated and demonstrated greater stability under dry hydrogen atmospheres. However, Zr substitution results in a tradeoff with electrical properties.     

Ferromagnetic Ordering of Energy Levels for {U_q(\mathfrak{sl}_2)} Symmetric Spin Chains

We consider the class of quantum spin chains with arbitrary ${U_{q}(\mathfrak{sl}_{2})}$ -invariant nearest-neighbor interactions, sometimes called SU _q (2) for the quantum deformation of SU(2), for q >?0. We derive sufficient conditions for the Hamiltonian to satisfy the property we call ferromagnetic ordering of energy levels. This is the property that the ground state energy restricted to a fixed total spin subspace is a decreasing function of the total spin. Using the Perron?CFrobenius theorem, we show sufficient conditions are positivity of all interactions in the dual canonical basis of Lusztig. We characterize the cone of positive interactions, showing that it is a simplicial cone consisting of all non-positive linear combinations of ??cascade operators,?? a special new basis of ${U_{q}(\mathfrak{sl}_2)}$ intertwiners we define.     

Effect of temperature on $$\mathbf{In}_{{\varvec{x}}} \mathbf{Ga}_{1-{{\varvec{x}}}} \mathbf{As}/\mathbf{GaAs}$$ quantum dots

Analytical solution of the Dirac equation for the modified Pöschl–Teller potential and trigonometric Scarf II non-central potential for spin symmetry is studied using asymptotic iteration method. One-dimensional Dirac equation consisting of the radial and angular parts can be obtained by the separation of variables. By using asymptotic iteration method, the relativistic energy equation and orbital quantum number (l) equation can be obtained, where both are interrelated. Relativistic energy equation is calculated numerically by the Matlab software. The increase in the radial quantum number n _r causes a decrease in the energy value, and the wave functions of the radial and the angular parts are expressed in terms of hypergeometric functions. Some thermodynamical properties of the system can be determined by reducing the relativistic energy equation to the non-relativistic energy equation. Thermodynamical properties such as vibrational partition function, vibrational specific heat function and vibrational mean energy function are expressed in terms of error function.     

Schur Function Identities Arising From the Basic Representation of {A^{(2)}_{2}}

A Lie theoretic interpretation is given for some formulas of Schur functions and Schur Q-functions. Two realizations of the basic representation of the Lie algebra \({A^{(2)}_2}\) are considered; one is on the fermionic Fock space and the other is on the bosonic polynomial space. Via the boson–fermion correspondence, simple relations of the vacuum expectation values of fermions turn out to be algebraic relations of Schur functions.     

Form Factors of $${f}_{{1}}{(1285)}$$ Meson

Physics of Atomic Nuclei - Parameterizations of the electromagnetic form factors of $$f_{1}(1285)$$ meson are considered. Using these parameterizations theoretical predictions for the total cross...     

Effect of tensile and compressive strain on the magnetic ordering of the ($$\hbox {LaMnO}_{3})_{1}/\hbox {(SrTiO}_{3})_{1}$$ superlattice

We study the effects of tensile and compressive strain on the \((\hbox {LaMnO}_{3})_{1}/(\hbox {SrTiO}_{3})_{1}\) superlattice from density functional theory using Quantum-Espresso open source code. In the unstrained superlattice, electron interactions in out-of-plane Mn–O–Ti chains are dominated by superexchange interactions, giving rise to ferromagnetic and half-metallic conducting characters. We found that the most stable magnetic configuration is G-type antiferromagnetic configuration for strong compressive strain and for strong tensile strain it is A-type antiferromagnetic configuration. The results are in accordance with the experimental observations which show that the superlattices can be grown on different substrates, and due to the difference in lattice parameters of the substrate and the main layer, there are also changes in the amount of strain applied to the superlattice.     

Magnetic order in RCr\mathsf{_{2}}Si\mathsf{_{2}} intermetallics

The magnetic structure and ordering temperatures of three intermetallic compounds which crystallize in the tetragonal ThCr₂Si₂ structure, TbCr₂Si₂, HoCr₂Si₂ and ErCr₂Si₂, have been determined by neutron diffraction, differential scanning calorimetry and magnetization measurements. The Cr-sublattice orders anti-ferromagnetically with Néel temperatures of 758 K for TbCr₂Si₂, 718 K for HoCr₂Si₂ and 692 K for ErCr₂Si₂. Chromium atoms located at 4d crystallographic sites are aligned anti-parallel along the c-axis, with G_ZCr magnetic modes. In contrast with metallic bcc Cr, the refined room temperature value of the ordered Cr moment is anomalously large for all three compounds. No long range magnetic order of the R sublattice in TbCr₂Si₂ and HoCr₂Si₂ is observed, whilst the Er sublattice in ErCr₂Si₂ orders independently of the Cr sublattice below 2.4 K with moments ferromagnetically aligned in the basal plane.Received: 4 November 2003, Published online: 30 January 2004PACS: 75.25. + z Spin arrangements in magnetically ordered materials (including neutron and spin-polarized electron studies, synchrotron-source X-ray scattering, etc.) - 75.30.Cr Saturation moments and magnetic susceptibilities - 75.50.Ee Antiferromagnetics     

Lasing of optically pumped XeF and analysis of the spectrum of the laser transitionB^2 \sum _{{1 \mathord{\left/ {\vphantom {1 2}} \right. \kern-\nulldelimiterspace} 2}}^ + - X^2 \sum _{{1 \mathord{\left/ {\vphantom {1 2}} \right. \kern-\nulldelimiterspace} 2}}^ +

The operating principle of a photodissociation XeF laser (λ?350 nm) is discussed. A laser operating on the gas mixture XeF₂:N₂(SF₆):Ar pumped by radiation from an open high-current discharge is described. The maximum lasing duration is 5 μsec, the maximum output energy is 0.15 J. The vibrational structure of the XeF-molecule transition B²Σ_1/2 ⁺ ? X²Σ_1/2 ⁺, observed in absorption, luminescence, and stimulated emission, is investlgated. The vibrational quantum and the anharmonicity in the upper and lower states are measured: ω_e ^' = 308.7 cm^-1, ω_e ^'x_e ^' = 1.44 cm^-1, ω_e ^'' = 225.7 cm^-1, ω_e ^''x_e ^'' = 11.0 cm^-1. The difference between the equilibrium internuclear distances of the XeF molecule is determined for the excited (B) and ground (X) states, namely r_e ^' - r_e ^'' = 0.33 +- 0.01 Å.     

Microwave fluctuational conductivity in YBa\mathsf{_{2}}Cu\mathsf{_{3}}O \mathsf{_{7-\delta}}

We present measurements of the microwave complex conductivity at 23.9 and 48.2 GHz in YBa₂Cu₃O $_{7-\delta}$ films, in the fluctuational region above T _c . With increasing temperature, the fluctuational excess conductivity drops much faster than the well-known calculations within the time-dependent Ginzburg-Landau theory [H. Schmidt, Z. Phys. 216, 336 (1968)]. Approaching the transition temperature, slowing down of the fluctuations is observed. We discuss the results in terms of a modified Gaussian theory for finite-frequency fluctuational conductivity, where renormalization is introduced in order to account for the $T\rightarrow T_{c}$ regime, and a spectral cutoff is inserted in order to discard high-momentum modes. The data are in excellent agreement with the modified theory, when formulated for three-dimensional, anisotropic superconductors, in the whole experimentally accessible temperature range, and for both frequencies.