Two-component abelian sandpile models

In one-component abelian sandpile models, the toppling probabilities are independent quantities. This is not the case in multi-component models. The condition of associativity of the underlying abelian algebras impose nonlinear relations among the toppling probabilities. These relations are derived for the case of two-component quadratic abelian algebras. We show that abelian sandpile models with two conservation laws have only trivial avalanches.Comment: Final version. To appear in Phys.Rev.

On R-matrix representations of Birman-Murakami-Wenzl algebras

We show that to every local representation of the Birman-Murakami-Wenzl algebra defined by a skew-invertible R-matrix $R\in Aut(V\otimes V)$ one can associate pairings $V\otimes V\to C$ and $V^*\otimes V^*\to C$, where V is the representation space. Further, we investigate conditions under which the corresponding quantum group is of SO or Sp type.Comment: 9 page

On quantum matrix algebras satisfying the Cayley-Hamilton-Newton identities

The Cayley-Hamilton-Newton identities which generalize both the characteristic identity and the Newton relations have been recently obtained for the algebras of the RTT-type. We extend this result to a wider class of algebras M(R,F) defined by a pair of compatible solutions of the Yang-Baxter equation. This class includes the RTT-algebras as well as the Reflection equation algebras

Modified Affine Hecke Algebras and Drinfeldians of Type A

We introduce a modified affine Hecke algebra \h{H}^{+}_{q\eta}({l}) (\h{H}_{q\eta}({l})) which depends on two deformation parameters $q$ and $\eta$. When the parameter $\eta$ is equal to zero the algebra \h{H}_{q\eta=0}(l) coincides with the usual affine Hecke algebra \h{H}_{q}(l) of type $A_{l-1}$, if the parameter q goes to 1 the algebra \h{H}^{+}_{q=1\eta}(l) is isomorphic to the degenerate affine Hecke algebra \Lm_{\eta}(l) introduced by Drinfeld. We construct a functor from a category of representations of $H_{q\eta}^{+}(l)$ into a category of representations of Drinfeldian $D_{q\eta}(sl(n+1))$ which has been introduced by the first author.Comment: 11 pages, LATEX. Contribution to Proceedings "Quantum Theory and Symmetries" (Goslar, July 18-22, 1999) (World Scientific, 2000

The pair annihilation reaction D + D --> 0 in disordered media and conformal invariance

The raise and peel model describes the stochastic model of a fluctuating interface separating a substrate covered with clusters of matter of different sizes, and a rarefied gas of tiles. The stationary state is obtained when adsorption compensates the desorption of tiles. This model is generalized to an interface with defects (D). The defects are either adjacent or separated by a cluster. If a tile hits the end of a cluster with a defect nearby, the defect hops at the other end of the cluster changing its shape. If a tile hits two adjacent defects, the defect annihilate and are replaced by a small cluster. There are no defects in the stationary state. This model can be seen as describing the reaction D + D -->0, in which the particles (defects) D hop at long distances changing the medium and annihilate. Between the hops the medium also changes (tiles hit clusters changing their shapes). Several properties of this model are presented and some exact results are obtained using the connection of our model with a conformal invariant quantum chain.Comment: 8 pages, 12figure

Local energy-density functional approach to many-body nuclear systems with s-wave pairing

The ground-state properties of superfluid nuclear systems with ^1S_0 pairing are studied within a local energy-density functional (LEDF) approach. A new form of the LEDF is proposed with a volume part which fits the Friedman- Pandharipande and Wiringa-Fiks-Fabrocini equation of state at low and moderate densities and allows an extrapolation to higher densities preserving causality. For inhomogeneous systems, a surface term with two free parameters is added. In addition to the Coulomb direct and exchange interaction energy, an effective density-dependent Coulomb-nuclear correlation term is included with one more free parameter, giving a contribution of the same order of magnitude as the Nolen-Schiffer anomaly in Coulomb displacement energy. The root-mean-square deviations from experimental masses and radii with the proposed LEDF come out about a factor of two smaller than those obtained with the conventional functionals based on the Skyrme or finite-range Gogny force, or on the relativistic mean-field theory. The generalized variational principle is formulated leading to the self-consistent Gor'kov equations which are solved exactly, with physical boundary conditions both for the bound and scattering states. With a zero-range density-dependent cutoff pairing interaction incorporating a density-gradient term, the evolution of differential observables such as odd-even mass differences and staggering in charge radii, is reproduced reasonably well, including kinks at magic neutron numbers. An extrapolation to infinite nuclear matter is discussed. We study also the dilute limit in both the weak and strong coupling regime.Comment: 19 pages, 8 figures. LaTeX, with modified cls file supplied. To be published in vol. 3 of the series "Advances in Quantum Many-Body Theory", World Scientific (Proceedings of the MBX Conference, Seattle, September 10-15, 1999

Supersymmetry on Jacobstahl lattices

It is shown that the construction of Yang and Fendley (2004 {\it J. Phys. A: Math.Gen. {\bf 37}} 8937) to obtainsupersymmetric systems, leads not to the open XXZ chain with anisotropy $\Delta =-{1/2}$ but to systems having dimensions given by Jacobstahl sequences.For each system the ground state is unique. The continuum limit of the spectra of the Jacobstahl systems coincide, up to degeneracies, with that of the $U_q(sl(2))$ invariant XXZ chain for $q=\exp(i\pi/3)$. The relation between the Jacobstahl systems and the open XXZ chain is explained.Comment: 6 pages, 0 figure

The Effect of the Pairing Interaction on the Energies of Isobar Analog Resonances in 112−124^{112-124}Sb and Isospin Admixture in 100−124^{100-124}Sn Isotopes

In the present study, the effect of the pairing interaction and the isovector correlation between nucleons on the properties of the isobar analog resonances (IAR) in $^{112-124}$Sb isotopes and the isospin admixture in $^{100-124}$Sn isotopes is investigated within the framework of the quasiparticle random phase approximation (QRPA). The form of the interaction strength parameter is related to the shell model potential by restoring the isotopic invariance of the nuclear part of the total Hamiltonian. In this respect, the isospin admixtures in the $^{100-124}$Sn isotopes are calculated, and the dependence of the differential cross section and the volume integral $J_{F}$ for the Sn($^{3}$He,t)Sb reactions at E($^{3}$He)$=200$ MeV occurring by the excitation of IAR on mass number A is examined. Our results show that the calculated value for the isospin mixing in the $^{100}$Sn isotope is in good agreement with Colo et al.'s estimates $(4-5$, and the obtained values for the volume integral change within the error range of the value reported by Fujiwara et al. (53$\pm$5 MeV fm$^{3}$). Moreover, it is concluded that although the differential cross section of the isobar analog resonance for the ($^{3}$He,t) reactions is not sensitive to pairing correlations between nucleons, a considerable effect on the isospin admixtures in $N\approx Z$ isotopes can be seen with the presence of these correlations.Comment: 16 pages, 5 EPS figures and 2 tables, Late

Different facets of the raise and peel model

The raise and peel model is a one-dimensional stochastic model of a fluctuating interface with nonlocal interactions. This is an interesting physical model. It's phase diagram has a massive phase and a gapless phase with varying critical exponents. At the phase transition point, the model exhibits conformal invariance which is a space-time symmetry. Also at this point the model has several other facets which are the connections to associative algebras, two-dimensional fully packed loop models and combinatorics.Comment: 29 pages 17 figure

Refined Razumov-Stroganov conjectures for open boundaries

Recently it has been conjectured that the ground-state of a Markovian Hamiltonian, with one boundary operator, acting in a link pattern space is related to vertically and horizontally symmetric alternating-sign matrices (equivalently fully-packed loop configurations (FPL) on a grid with special boundaries).We extend this conjecture by introducing an arbitrary boundary parameter. We show that the parameter dependent ground state is related to refined vertically symmetric alternating-sign matrices i.e. with prescribed configurations (respectively, prescribed FPL configurations) in the next to central row. We also conjecture a relation between the ground-state of a Markovian Hamiltonian with two boundary operators and arbitrary coefficients and some doubly refined (dependence on two parameters) FPL configurations. Our conjectures might be useful in the study of ground-states of the O(1) and XXZ models, as well as the stationary states of Raise and Peel models.Comment: 11 pages LaTeX, 8 postscript figure