Exact solution at integrable coupling of a model for the Josephson effect between small metallic grains

A model is introduced for two reduced BCS systems which are coupled through the transfer of Cooper pairs between the systems. The model may thus be used in the analysis of the Josephson effect arising from pair tunneling between two strongly coupled small metallic grains. At a particular coupling strength the model is integrable and explicit results are derived for the energy spectrum, conserved operators, integrals of motion, and wave function scalar products. It is also shown that form factors can be obtained for the calculation of correlation functions. Further, a connection with perturbed conformal field theory is made.Comment: 12 pages, latex, no figure

The structural, mechanical, electronic, optical and thermodynamic properties of t-X3_{3}As4_{4} (X == Si, Ge and Sn) by first-principles calculations

The structural, mechanical, electronic, optical and thermodynamic properties of the t-X$_{\mathrm{3}}$As$_{\mathrm{4}}$ (X $=$ Si, Ge and Sn) with tetragonal structure have been investigated by first principles calculations. Our calculated results show that these compounds are mechanically and dynamically stable. By the study of elastic anisotropy, it is found that the anisotropic of the t-Sn$_{\mathrm{3}}$As$_{\mathrm{4}}$ is stronger than that of t-Si$_{\mathrm{3}}$As$_{\mathrm{4}}$ and t-Ge$_{\mathrm{3}}$As$_{\mathrm{4}}$. The band structures and density of states show that the t-X$_{\mathrm{3}}$As$_{\mathrm{4}}$ (Si, Ge and Sn) are semiconductors with narrow band gaps. Based on the analyses of electron density difference, in t-X$_{\mathrm{3}}$As$_{\mathrm{4}}$ As atoms get electrons, X atoms lose electrons. The calculated static dielectric constants, $\varepsilon_{1} (0)$, are 15.5, 20.0 and 15.1 eV for t-X$_{\mathrm{3}}$As$_{\mathrm{4}}$ (X $=$ Si, Ge and Sn), respectively. The Dulong-Petit limit of t-X$_{\mathrm{3}}$As$_{\mathrm{4}}$ is about 10 J mol$^{\mathrm{-1}}$K$^{\mathrm{-1}}$. The thermodynamic stability successively decreases from t-Si$_{\mathrm{3}}$As$_{\mathrm{4}}$ to t-Ge$_{\mathrm{3}}$As$_{\mathrm{4}}$ to t-Sn$_{\mathrm{3}}$As$_{\mathrm{4}}$.Comment: 14 pages, 10 figures, 6 table

Graded reflection equation algebras and integrable Kondo impurities in the one-dimensional t-J model

Integrable Kondo impurities in two cases of the one-dimensional $t-J$ model are studied by means of the boundary ${\bf Z}_2$-graded quantum inverse scattering method. The boundary $K$ matrices depending on the local magnetic moments of the impurities are presented as nontrivial realizations of the reflection equation algebras in an impurity Hilbert space. Furthermore, these models are solved by using the algebraic Bethe ansatz method and the Bethe ansatz equations are obtained.Comment: 14 pages, RevTe