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

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

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

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

Influence of Quantum Hall Effect on Linear and Nonlinear Conductivity in the FISDW States of the Organic Conductor (TMTSF)_2PF_6

We report a detailed characterization of quantum Hall effect (QHE) influence on the linear and non-linear resistivity tensor in FISDW phases of the organic conductor (TMTSF)2PF6. We show that the behavior at low electric fields, observed for nominally pure single crystals with different values of the resistivity ratio, is fully consistent with a theoretical model, which takes QHE nature of FISDW and residual quasi-particle density associated with different crystal imperfection levels into account. The non-linearity in longitudinal and diagonal resistivity tensor components observed at large electric fields reconciles preceding contradictory results. Our theoretical model offers a qualitatively good explanation of the observed features if a sliding of the density wave with the concomitant destruction of QHE, switched on above a finite electric field, is taken into account.Comment: 8 pages, 6 figures, submitted to EPJ

The BCS theory of q-deformed nucleon pairs - qBCS

We construct a coherent state of q-deformed zero coupled nucleon pairs distributed in several single-particle orbits. Using a variational approach, the set of equations of qBCS theory, to be solved self consistently for occupation probabilities, gap parameter Delta, and the chemical potential lambda, is obtained. Results for valence nucleons in nuclear degenerate sdg major shell show that the strongly coupled zero angular momentum nucleon pairs can be substituted by weakly coupled q-deformed zero angular momentum nucleon pairs. A study of Sn isotopes reveals a well defined universe of (G, q) values, for which qBCS converges. While the qBCS and BCS show similar results for Gap parameter Delta in Sn isotopes, the ground state energies are lower in qBCS. The pairing correlations in N nucleon system, increase with increasing q (for q real).Comment: 8 pages, REVTEX, 3 eps figure