Clifford-Gegenbauer polynomials related to the Dunkl Dirac operator

We introduce the so-called Clifford-Gegenbauer polynomials in the framework of Dunkl operators, as well on the unit ball B(1), as on the Euclidean space $R^m$. In both cases we obtain several properties of these polynomials, such as a Rodrigues formula, a differential equation and an explicit relation connecting them with the Jacobi polynomials on the real line. As in the classical Clifford case, the orthogonality of the polynomials on $R^m$ must be treated in a completely different way than the orthogonality of their counterparts on B(1). In case of $R^m$, it must be expressed in terms of a bilinear form instead of an integral. Furthermore, in this paper the theory of Dunkl monogenics is further developed.Comment: 19 pages, accepted for publication in Bulletin of the BM

Phase diagram of two-component dipolar fermions in one-dimensional optical lattices

We theoretically map out the ground state phase diagram of interacting dipolar fermions in one-dimensional lattice. Using a bosonization theory in the weak coupling limit at half filing, we show that one can construct a rich phase diagram by changing the angle between the lattice orientation and the polarization direction of the dipoles. In the strong coupling limit, at a general filing factor, we employ a variational approach and find that the emergence of a Wigner crystal phases. The structure factor provides clear signatures of the particle ordering in the Wigner crystal phases.Comment: Published Version (Physics Letters A

The Semantic Grid: A future e-Science infrastructure

e-Science offers a promising vision of how computer and communication technology can support and enhance the scientific process. It does this by enabling scientists to generate, analyse, share and discuss their insights, experiments and results in an effective manner. The underlying computer infrastructure that provides these facilities is commonly referred to as the Grid. At this time, there are a number of grid applications being developed and there is a whole raft of computer technologies that provide fragments of the necessary functionality. However there is currently a major gap between these endeavours and the vision of e-Science in which there is a high degree of easy-to-use and seamless automation and in which there are flexible collaborations and computations on a global scale. To bridge this practice–aspiration divide, this paper presents a research agenda whose aim is to move from the current state of the art in e-Science infrastructure, to the future infrastructure that is needed to support the full richness of the e-Science vision. Here the future e-Science research infrastructure is termed the Semantic Grid (Semantic Grid to Grid is meant to connote a similar relationship to the one that exists between the Semantic Web and the Web). In particular, we present a conceptual architecture for the Semantic Grid. This architecture adopts a service-oriented perspective in which distinct stakeholders in the scientific process, represented as software agents, provide services to one another, under various service level agreements, in various forms of marketplace. We then focus predominantly on the issues concerned with the way that knowledge is acquired and used in such environments since we believe this is the key differentiator between current grid endeavours and those envisioned for the Semantic Grid

Occupation probabilities from quadrupole moments in the Sn region

It is shown that a simple BCS model with a quadrupole-quadrupole interaction provides a consistent description of the measured quadrupole moments of a sequence of odd-mass Sn and Cd isotopes and allows the extraction of the neutron single-particle occupation probabilities.Comment: 7 pages, 2 figure