A One Dimensional Ideal Gas of Spinons, or Some Exact Results on the XXX Spin Chain with Long Range Interaction

We describe a few properties of the XXX spin chain with long range interaction. The plan of these notes is: 1. The Hamiltonian 2. Symmetry of the model 3. The irreducible multiplets 4. The spectrum 5. Wave functions and statistics 6. The spinon description 7. The thermodynamicsComment: Latex. Talk given by the first author at the Cargese-1993 workshop "Strings, conformal models and Topological felds theorie

Landau levels in a 2D noncommutative space: matrix and quaternionic vector coherent states

The behavior of an electron in an external uniform electromagnetic background coupled to a harmonic potential, with noncommuting space coordinates, is considered in this work. The thermodynamics of the system is studied. Matrix vector coherent states (MVCS) as well as quaternionic vector coherent states (QVCS), satisfying required properties, are also constructed and discussed

Yang-Baxter equation in spin chains with long range interactions

We consider the $su(n)$ spin chains with long range interactions and the spin generalization of the Calogero-Sutherland models. We show that their properties derive from a transfer matrix obeying the Yang-Baxter equation. We obtain the expression of the conserved quantities and we diagonalize them.Comment: Saclay-t93/00

Scattering matrices and affine Hecke algebras

We construct the scattering matrices for an arbitrary Weyl group in terms of elementary operators which obey the generalised Yang-Baxter equation. We use this construction to obtain the affine Hecke algebras. The center of the affine Hecke algebras coincides with commuting Hamiltonians. These Hamiltonians have q-deformed affine Lie algebras as symmetry algebra.Comment: 22 pages, harvmac, no figures, Lecture at Schladming, March 4,11 199

Identification of a Candidate CD5 Homologue in the Amphibian Xenopus laevis

We identified a novel T cell Ag in the South African clawed toad (Xenopus laevis) by a mAb designated 2B1. This Ag is present in relatively high levels on most thymocytes, approximately 65% of splenocytes, 55% of PBL, and 65% of intestinal lymphocytes, but is rarely seen on IgM+ B cells in any of these tissues. Lymphocytes bearing the 2B1 Ag proliferate in response to stimulation with Con A or PHA, whereas the 2B1- lymphocytes are reactive to LPS. Biochemical analysis indicates that this Ag is a differentially phosphorylated glycoprotein of 71 to 82 kDa. The protein core of 64 kDa bears both N- and O-linked carbohydrate side chains. The amino-terminal protein sequence of the 2B1 Ag shares significant homology with both the macrophage scavenger receptor type 1 motif and the mammalian CD5/CD6 family. The biochemical characteristics and cellular distribution of the 2B1 Ag suggest that it represents the CD5 homologue in X. laevis. While T cells constitutively express this highly conserved molecule, Xenopus B cells acquire the CD5 homologue only when they are stimulated in the presence of T cell

Lattice realizations of unitary minimal modular invariant partition functions

The conformal spectra of the critical dilute A-D-E lattice models are studied numerically. The results strongly indicate that, in branches 1 and 2, these models provide realizations of the complete A-D-E classification of unitary minimal modular invariant partition functions given by Cappelli, Itzykson and Zuber. In branches 3 and 4 the results indicate that the modular invariant partition functions factorize. Similar factorization results are also obtained for two-colour lattice models.Comment: 18 pages, Latex, with minor corrections and clarification

Coexistence of Superconductivity and Spin Density Wave orderings in the organic superconductor (TMTSF)_2PF_6

The phase diagram of the organic superconductor (TMTSF)_2PF_6 has been revisited using transport measurements with an improved control of the applied pressure. We have found a 0.8 kbar wide pressure domain below the critical point (9.43 kbar, 1.2 K) for the stabilisation of the superconducting ground state featuring a coexistence regime between spin density wave (SDW) and superconductivity (SC). The inhomogeneous character of the said pressure domain is supported by the analysis of the resistivity between T_SDW and T_SC and the superconducting critical current. The onset temperature T_SC is practically constant (1.20+-0.01 K) in this region where only the SC/SDW domain proportion below T_SC is increasing under pressure. An homogeneous superconducting state is recovered above the critical pressure with T_SC falling at increasing pressure. We propose a model comparing the free energy of a phase exhibiting a segregation between SDW and SC domains and the free energy of homogeneous phases which explains fairly well our experimental findings.Comment: 13 pages, 10 figures, revised v: fig.9 added, section 4.2 rewritten, accepted v: sections 4&5 improve