Rational r-matrices,higher rank Lie algebras and integrable proton–neutron BCS models

We study integrable cases of pairing BCS hamiltonians containing several types of fermions. We prove that there exist three classes of such integrable models associated with classical rational r  -matrices and Lie algebras gl(2m)$\mathit{gl}(2m)$, sp(2m)$\mathit{sp}(2m)$ and so(2m)$\mathit{so}(2m)$ correspondingly. We diagonalize the constructed hamiltonians by means of the algebraic Bethe ansatz. In the partial case of two types of fermions (m=2$m=2$) the obtained models may be interpreted as N=Z$N=Z$ proton–neutron integrable models. In particular, in the case of sp(4)$\mathit{sp}(4)$ we recover the famous integrable proton–neutron model of Richardson.     

Generalized Knizhnik–Zamolodchikov equations,off-shell Bethe ansatz and non-skew-symmetric classical r-matrices

Using non-skew-symmetric sl(2)$\mathit{sl}(2)$-valued classical r-matrices with spectral parameters we construct a generalization of the Knizhnik–Zamolodchikov (KZ) equations. We obtain integral solutions of the constructed KZ-type equations using the “off-shell” Bethe ansatz technique. We consider several examples of the obtained generalized KZ equations and their integral solutions that correspond to the “K-twisted” non-skew-symmetric classical r-matrices parametrized by arbitrary complex parameter ξ.     

Spin chains in magnetic field,non-skew-symmetric classical r-matrices and BCS-type integrable systems

We construct generalized Gaudin systems in an external magnetic field corresponding to arbitrary so(3)$\mathit{so}(3)$-valued non-skew-symmetric r-matrices with spectral parameters and non-homogeneous external magnetic fields. In the case of r  -matrices diagonal in the sl(2)$\mathit{sl}(2)$ basis we calculate the spectrum and the eigen-values of the corresponding generalized Gaudin hamiltonians using the algebraic Bethe ansatz. We explicitly consider several one-parametric families of non-skew-symmetric classical r-matrices and the corresponding generalized Gaudin systems in a magnetic field. We apply these results to fermionic systems and obtain a wide class of new integrable fermionic BCS-type hamiltonians.     

Franck-Condon factors and r-centroids of B-X, C-X and C-A band systems of AlO molecule

Using the high resolution Fourier transform spectrometer the B²Σ⁺-X²Σ⁺ band system of AlO molecule has been recorded. The rotational structure of eighteen bands belonging to B²Σ⁺-X²Σ⁺ transition of AlO have been analyzed which led to accurate rotational and vibrational constants of ground and excited states. A few bands, viz. (2, 1), (3, 2), (4, 3), (2, 3), (3, 4), (4, 5), and (5, 6) were analyzed for the first time. Using these constants, the Franck-Condon factors and r-centroids were computed for the bands of B-X, C-X and C-A band systems for the v′ = 0-8; v″ = 0-8 matrix using the method developed by Jarmain and Nicholls. The F-C factors and r-centroids obey the established relationships.     

Separation of variables for integrable spin–boson models

We formulate the functional Bethe ansatz for bosonic (infinite dimensional) representations of the Yang–Baxter algebra. The main deviation from the standard approach consists in a half infinite Sklyanin lattice made of the eigenvalues of the operator zeros of the Bethe annihilation operator. By a separation of variables, functional TQ-equations are obtained for this half infinite lattice. They provide valuable information about the spectrum of a given Hamiltonian model. We apply this procedure to integrable spin–boson models subject to both twisted and open boundary conditions. In the case of general twisted and certain open boundary conditions polynomial solutions to these TQ-equations are found and we compute the spectrum of both the full transfer matrix and its quasi-classical limit. For generic open boundaries we present a two-parameter family of Bethe equations, derived from TQ-equations that are compatible with polynomial solutions for Q. A connection of these parameters to the boundary fields is still missing.     

Explicit N-fold Darboux transformation for the classical Boussinesq system and multi-soliton solutions

In this Letter, a systematic method is presented to construct the N-fold Darboux transformation with multi-parameters for a spectral problem associated with a classical Boussinesq system. As an application, we obtain the new soliton solutions of the classical Boussinesq system.     

Higher order solutions of Lieb-Liniger integral equation

We study higher order solutions of Lieb-Liniger integral equation for a one-dimensional δ-function Bose gas. By use of the power series expansion method, the integral equation is solved and the correction terms which improve the Bogoliubov theory are calculated analytically in the weak coupling regime. Physical quantities such as the ground state energy and the chemical potential are represented by a dimensionless parameter γ=c/ρ, where c is the interaction strength and ρ is the number density of particles while the quasi-momentum distribution function is expressed in terms of a dimensionless parameter λ=c/K, where K is the cut-off momentum.     

Fourier transform microwave spectroscopy of isotopically substituted diacetylenes: rs-structure, quadrupole coupling, and anisotropic nuclear spin-spin interaction

Monodeuterated diacetylene (HCCCCD) and its ¹³C-substituted species H¹³CCCCD, HC¹³CCCD, HCC¹³CCD, and HCCC¹³CD were investigated by Fourier transform microwave spectroscopy. The D nuclear quadrupole splittings were almost completely resolved. For H¹³CCCCD hyperfine splittings caused by the anisotropic nuclear spin-spin interaction between the H and ¹³C nuclei were also observed. The analysis yielded rotational constants, centrifugal distortion constants, and the constants for the nuclear quadrupole coupling and anisotropic nuclear spin-spin interaction. The substitution structure of HCCCCD was calculated as follows: r_s(C-H) = 1.056054(39) Å, r_s(CC) = 1.208631(4) Å, r_s(C-C) = 1.374117(6) Å, r_s(CC) = 1.208116(4) Å, and r_s(C-D) = 1.056231(17) Å, in the order of the arrangement of the bonds. A rough estimate of the equilibrium structure is also presented. The eQq constant for the deuterium nucleus is 0.2061(4) MHz. The anisotropic ¹³C-H spin-spin interaction constant was experimentally determined for the first time as b = −29.2(15) kHz, which is defined as the coefficient of (3I_2zI_3z − I₂ · I₃), where I₂ and I₃ denote the H and ¹³C nuclear spins, respectively, and I_2z and I_3z their components along the molecular axis. The observed b constant is not accounted for by the direct magnetic dipole-dipole interaction only, suggesting a significant contribution from indirect anisotropic interaction.     

The high temperature expansion of the classical XYZ chain

The β$\beta$-expansion of the Helmholtz free energy (HFE) up to order β¹²${\beta }^{12}$ of the classical XYZ model with a single-ion anisotropy term and external magnetic field is calculated and compared to the numerical solution of Joyce's [Phys. Rev. Lett. 19 (1967) 581] for the XXZ   classical model, with neither single-ion anisotropy term nor external magnetic field. This comparison shows that the derived analytical expansion is valid for intermediate temperatures such as kT/_Jx≈0.5$\mathit{kT}/J_x\approx 0.5$. The specific heat and magnetic susceptibility of the S=2$S=2$ antiferromagnetic chain can be approximated by their respective classical results, within an error of 2.5%$2.5\%$, up to kT/J≈0.8$\mathit{kT}/J\approx 0.8$. For a vanishing external magnetic field the ferromagnetic and antiferromagnetic chains are shown to have the same classical HFE; their behaviour in a non-vanishing external magnetic field is also described.     

Erratum to “The extended Higgs system in R-symmetric supersymmetry theories” [Phys. Lett. B 697 (2011) 215]

We correct Fig. 1(right) of S.Y. Choi et al. (2011) [1] illustrating the neutralino masses in the R-symmetric model.     

Thermodynamic investigations of ternary o-toluidine + tetrahydropyran + N,N-dimethylformamide mixture and its binaries at 298.15, 303.15 and 308.15 K

The densities ρ, speed of sound u, data of o-toluidine (i) + tetrahydropyran (j) + N,N-dimethylformamide (k) and its {tetrahydropyran (j) + N,N-dimethylformamide (k); o-toluidine (i) + N,N-dimethylformamide (k)} binaries have been measured as a function of composition at 298.15, 303.15 and 308.15 K. The excess molar enthalpies, H^E data of same set of binary mixtures have also been measured over entire composition at 308.15 K. The densities and speeds of sound data of binary and ternary mixtures have been utilized to determine their excess molar volumes, V^E and excess isentropic compressibilities, κ_S^E. The observed thermodynamic properties of binary and ternary mixtures have been analyzed in terms of Graph theory. It has been observed that Graph theory correctly predicts the sign as well as magnitude of thermodynamic properties.     

Integrable perturbations of the N-dimensional isotropic oscillator

Two new families of completely integrable perturbations of the N-dimensional isotropic harmonic oscillator Hamiltonian are presented. Such perturbations depend on arbitrary functions and N free parameters and their integrals of motion are explicitly constructed by making use of an underlying h₆-coalgebra symmetry. Several known integrable Hamiltonians in low dimensions are obtained as particular specializations of the general results here presented. An alternative route for the integrability of all these systems is provided by a suitable canonical transformation which, in turn, opens the possibility of adding (N−1) ‘Rosochatius’ terms that preserve the complete integrability of all these models.     

Spectroscopy of X2Y4 (D2h) molecules: tensorial formalism adapted to the O(3)⊃D2h chain, Hamiltonian and transition moment operators

A tensorial formalism adapted to the case of the X₂Y₄ molecules with D_2h symmetry has been developed in the same way as in the previous works on XY₄ (T_d) and XY₆ (O_h) spherical tops and XY₅Z (C_4v) symmetric tops. Here, we use the O(3)⊃D_2h group chain. All the coupling coefficients and formulas for the computation of matrix elements are given for this chain and used in the case of the Hamiltonian and transition moment operators.     

Near room temperature magnetocaloric properties of melt-spun Gd100−xBx (x=0, 5, 10, 15, and 20 at%) alloys

The magnetocaloric properties of melt-spun Gd-B alloys were examined with the aim to explore their potential application as magnetic refrigerants near room temperature. A series of Gd_100−xB_x (x=0, 5, 10, 15, and 20 at%) alloys were prepared by melt spinning. With the decrease in Gd/B ratio, Curie temperature (T_C) remains constant at ∼293 K, and saturation magnetization, at 275 K, decreases from ∼100 to ∼78 emu/g. Negligible magnetic hysteresis was observed in these alloys. The peak value of magnetic entropy change, (−ΔS_M)_max, decreased from ∼9.9 J/kg K (0-5 T) and ∼5.5 J/kg K (0-2 T) for melt-spun Gd to ∼7.7 J/kg K (0-5 T) and ∼4.0 J/kg K (0-2 T), respectively for melt-spun Gd₈₅B₁₅ and Gd₈₀B₂₀ alloys. Similarly, the refrigeration capacity (q) decreased monotonously from ∼430 J/kg (0-5 T) for melt-spun Gd to ∼330 J/kg (0-5 T) for melt-spun Gd₈₀B₂₀ alloy. The near room temperature magnetocaloric properties of melt-spun Gd_100−xB_x (0≤x≤20) alloys were found to be comparable to few first-order transition based magnetic refrigerants.     

Microwave structural studies of organoselenium compounds 1. Microwave spectra, molecular structure, and methyl barrier to internal rotation of dimethyl diselenide

The rotational spectra of nine isotopomers of dimethyl diselenide, CH₃SeSeCH₃, have been measured with a molecular-beam Fourier transform microwave spectrometer. The spectra were complex due to the presence of many isotopomers in natural abundance and the splitting caused by the interactions with two methyl internal rotors. The spectra were assigned and fit to experimental precision to an effective rotational Hamiltonian for molecules with two periodic internal motions. The spectra of the symmetric isotopomers are consistent with a C₂ equilibrium structure. The rotational constants were used to determine the r_s structure of the C-Se-Se-C frame with the results r(SeSe)=2.306(3) Å, r(SeC)=1.954(6) Å, ?(CSeSe)=99.8(2)°, ?(CSeSeC)=85.2(1)°. A barrier to internal rotation of the methyl groups of 395 ± 2 cm⁻¹ was derived from the internal rotation splittings.     

Planar nano-block structures Tin+1Al0.5Cn and Tin+1Cn (n = 1, and 2) from MAX phases: Structural,electronic properties and relative stability from first principles calculations

Structural, electronic properties and relative stability of quasi-two-dimensional (2D) free-standing planar nano-block (NBs) structures Ti_n+1Al_0.5C_n and Ti_n+1C_n (n = 1 and 2), which can be prepared using the recently developed procedure of exfoliation of corresponding NBs from MAX phases, were examined within first principles calculations in comparison with parent MAX phases Ti₃AlC₂ and Ti₂AlC. We found that in general Ti_n+1C_n and Ti_n+1Al_0.5C_n NBs retain the atomic geometries of the corresponding blocks of the MAX phases, but some structural distortions for the NBs occur owing to the lowering of the coordination number for atoms in the external Ti sheets of the nano-block structures. Our analysis based on their cohesive and formation energies reveals that the stability of the nano-block structures increases with index n (or, in other words, with a growth of the number of Ti–C bonds), the Al-containing NBs becoming more stable than the “pure” Ti–C NBs. Our data show that the magnetization of the simulated planar nano-block structures can be expected; so, for the Ti₃C₂ nano-block the most stable will be the spin configuration, where within each external Ti sheet the spins are coupled ferromagnetically together with antiferromagnetic ordering between opposite external titanium sheets of this nano-block.     

Phase stability,elastic, electronic,thermal and optical properties of Ti3Al1−xSixC2 (0≤x≤1): First principle study

The structural parameters with stability upon Si incorporation and elastic, electronic, thermodynamic and optical properties of Ti₃Al_1−xSi_xC₂ (0≤x≤1) are investigated systematically by the plane wave pseudopotential method based on the density functional theory (DFT). The increase of some elastic parameters with increasing Si-content renders the alloys to possess higher compressive and tensile strength. The Vickers hardness value obtained with the help of Mulliken population analysis increases as x is increased from 0 to 1. The solid solutions considered are all metallic with valence and conduction bands, which have a mainly Ti 3d character, crossing the Fermi level. The temperature and pressure dependences of bulk modulus, normalized volume, specific heats, thermal expansion coefficient, and Debye temperature are all obtained through the quasi-harmonic Debye model with phononic effects for T=0−1000 K and P=0−50 GPa. The obtained results are compared with other results available. Further an analysis of optical functions for two polarization vectors reveals that the reflectivity is high in the visible–ultraviolet region up to ∼10.5 eV region showing promise as a good coating material.     

Structural and magnetic properties in Bi1−xRxFeO3 (x=0-1, R=La, Nd, Sm, Eu and Tb) polycrystalline ceramics

A series of rare-earth doped BiFeO₃ samples, Bi_1−xR_xFeO₃ (x=0-1, R=La, Nd, Sm, Eu and Tb), were prepared in this work. X-ray diffraction analysis showed that the structure of rare-earth doped BiFeO₃ was transformed from rhombohedral lattice to orthorhombic one by increasing x. The lattice constants and unit-cell volume decreased with the increasing of the doping content, while both the Néel temperature and magnetization were enhanced. A magnetic phase transition was observed at about 35 K for BiFeO₃. The variation of the magnetization with temperature depended on applied field strength and magnetizing history, which was explained according to the antiferromagnetic exchange interaction between Fe and R sites in Bi_1−xR_xFeO₃(x>0). The magnetocrystalline anisotropy contributed by Fe sublattice gave rise to a large coercivity in Bi_xNd_1−xFeO₃ with an orthorhombic structure.