[en] The quantum version of the direct and inverse problem of the inverse scattering transform for the nonlinear Schroedinger model of spin-1/2 particles with attractive coupling are investigated. The Yang-Baxter equations are solved to get various commutation relations; the energy spectrum and the quantum Gelfand-levitan equations are obtained. (orig.)

[en] We show that in the translation invariant case and in the antiferromagnetic phase the reduced density matrix ρ₂ has no off-diagonal long-range order of on-site electron pairs for the single-band Hubbard model on a cubic lattice away from half filling at finite temperatures both for the positive coupling and for the negative coupling. In these cases the model cannot give a mechanism for the superconductivity caused by the condensation of on-site electron pairs and the nearest-neighbor electron pairs. ((orig.))

[en] Relations between the existence of ODLRO in the reduced density matrix ρ_n (for all n ≥ 1) and that of superconducting currents in a hollow cylinder is discussed. Some concrete behaviours of ρ_n, including the power lay decaying behaviour, in the coordinate space representation are considered and the corresponding effective superconducting particle densities are given. Some restraint conditions caused by the existence of the ODLRO (including quasi-ODLRO) have been found and discussions on the minimum unit of flux quantization are also included. (author). 3 refs

[en] The Bethe ansatz equations for the multicomponent nonlinear Schroedinger model with supermatrices are obtained by using the quantum inverse scattering transform. (orig.)

[en] Some electromagnetic properties of the η-pairing eigenstate of the Hubbard model are investigated. The persistent current density J_s in the eigenstate is discussed, and the distribution of magnetic field in the studied periodic lattice is analyzed. It is shown that the behaviour of the electromagnetic response is peculiar

[en] In this note, we will argue that ODLRO may not be a sufficient condition for superconductivity logically on a lattice by means of an example. Meanwhile, we will point out that a state, possessing ODLRO, will be definitely superconducting if some certain conditions which we found are complied. (orig.)

[en] The quantum 2-component DS1 system was reduced to two 1D many-body problems with δ-function interactions, which were solved by Bethe ansatz. Using the ansatz of Pang, Pu and Zhao and introducing symmetric and antisymmetric Young operators of the permutation group, we obtain the exact solutions for the system. (author). 9 refs

[en] The analytic expression of the Wilson number of the Kondo model with arbitrary impurity spin is obtained. The Wilson number is the same for all impurity spins, contrary to the result in previous literatures