Link invariants from NN-state vertex models: an alternative construction independent of statistical models

We reproduce the hierarchy of link invariants associated to the series of $N$-state vertex models with a method different from the original construction due to Akutsu, Deguchi and Wadati. The alternative method substitutes the `crossing symmetry' property exhibited by the Boltzmann weights of the vertex models by a similar property which, for the purpose of constructing link invariants, encodes the same information but requires only the limit of the Boltzmann weights when the spectral parameter is sent to infinity.Comment: 20 pages, LaTeX, uses epsf.sty. To appear in Nucl. Phys.

Quartetting in Nuclear Matter

A general theory for the condensation of strongly bound quartets in infinite nuclear matter is presented. Critical temperatures for symmetric and asymmetric nuclear matter are evaluated. A fully nonlinear theory for the quartet order parameter, based on an analogy of the Gorkov approach to pairing, is presented and solved. The strong qualitative difference with pairing is pointed out

Many Body Theory for Quartets, Trions, and Pairs in Low Density Multi-Component Fermi-Systems

A selfconsistent many body approach for the description of gases with quartets, trions, and pairs is presented. Applications to 3D Fermi systems at low density are discussed

Spin Chains and Chiral Lattice Fermions

The generalization of Lorentz invariance to solvable two-dimensional lattice fermion models has been formulated in terms of Baxter's corner transfer matrix. In these models, the lattice Hamiltonian and boost operator are given by fermionized nearest-neighbor Heisenberg spin chain operators. The transformation properties of the local lattice fermion operators under a boost provide a natural and precise way of generalizing the chiral structure of a continuum Dirac field to the lattice. The resulting formulation differs from both the Wilson and staggered (Kogut-Susskind) prescriptions. In particular, an axial $Q_5$ rotation is sitewise local, while the vector charge rotation mixes nearest neighbors on even and odd sublattices.Comment: 3 pages, latex, no figure

Discrete Spinning Tops -- Difference equations for Euler, Lagrange, and Kowalevski tops

Several methods of time discretization are examined for integrable rigid body models, such as Euler, Lagrange, and Kowalevski tops. Problems of Lax-Moser pairs, conservation laws, and explicit solver algorithms are discussed. New discretization method is proposed for Kowalevski top, which have properties $\boldsymbol{\gamma}^2=1$, and the Kowalevski integral $|\xi|^2=\text{const.}$ satisfied exactly. Numerical tests are done successfully.Comment: 13 pages, 4 figure

An extension of Gauss's arithmetic-geometric mean (AGM) to three variables iteration scheme

Gauss's arithmetic-geometric mean (AGM) which is described by two variables iteration $(a_n, b_n)\rightarrow (a_{n+1}, b_{n+1})$ by $a_{n+1}=(a_n+b_n)/2,\ b_{n+1}=\sqrt{a_nb_n}$. We extend it to three variables iteration$(a_n, b_n, c_n)\rightarrow (a_{n+1}, b_{n+1}, c_{n+1})$which reduces to Gauss's AGM when$c_0=0$. Our iteration starting from$a_0>b_0>c_0>0$with further restriction$a_0>b_0+c_0$converges to$a_\infty=b_\infty=M(a_0, b_0, c_0)$and$c_\infty=0$. The limit$M(a_0, b_0, c_0)$is expressed by Appell's hyper-geometric function$F_1(1/2, \{1/2, 1/2\}, 1; \kappa, \lambda)$of two variables$(\kappa, \lambda)$which are determined by$(a_0, b_0, c_0)$. A relation between two hyper-geometric functions (Gauss's and Appell's) is found as a by-product.Comment: 10 pages, 0 figure

Phase space deformation of a trapped dipolar Fermi gas

We consider a system of quantum degenerate spin polarized fermions in a harmonic trap at zero temperature, interacting via dipole-dipole forces. We introduce a variational Wigner function to describe the deformation and compression of the Fermi gas in phase space and use it to examine the stability of the system. We emphasize the important roles played by the Fock exchange term of the dipolar interaction which results in a non-spherical Fermi surface.Comment: 5 pages, 5 figure

Exact solution for the spin-ss XXZ quantum chain with non-diagonal twists

We study integrable vertex models and quantum spin chains with toroidal boundary conditions. An interesting class of such boundaries is associated with non-diagonal twist matrices. For such models there are no trivial reference states upon which a Bethe ansatz calculation can be constructed, in contrast to the well-known case of periodic boundary conditions. In this paper we show how the transfer matrix eigenvalue expression for the spin-$s$ XXZ chain twisted by the charge-conjugation matrix can in fact be obtained. The technique used is the generalization to spin-$s$ of the functional relation method based on ``pair-propagation through a vertex''. The Bethe ansatz-type equations obtained reduce, in the case of lattice size $N=1$, to those recently found for the Hofstadter problem of Bloch electrons on a square lattice in a magnetic field.Comment: 25 pages, LaTe

On The Trajectory of Boko Haram Terrorism in Nigeria: Socio-Economic Challenges and Intervention Strategies for Conflict Resolution

Approximately a decade of Boko Haram catastrophic enterprises in Nigeria has described the Islamist terrorist group as an anathema to sustainable development as well as the nation’s most protracted stand-off of recent times. The study employed a qualitative methodological approach of in-depth interviews to examine the multi-faceted challenges of the crisis in Nigeria. The study unfolds a great deal of deplorable effects associated with gradual underdevelopment of the Nigerian state, particularly in the areas of socio-economic, political, religious, educational, agricultural, and health advancement of the country. With Boko Haram’s persistent enterprise flourishing in Nigeria and no lasting solutions hitherto in sight, the study recommends peaceful negotiation as an immediate response to the crisis and pre-emptive legal measures as a remote solution to address such problem should it arise in the nearest future