Derivations, isomorphisms, and second cohomology of generalized Witt algebras

Generalized Witt algebras, over a field of characteristic , were defined by Kawamoto about 12 years ago. Using different notations from Kawamoto's, we give an essentially equivalent definition of generalized Witt algebras over , where the ingredients are an abelian group , a vector space over , and a map which is linear in the first variable and additive in the second one. In this paper, the derivations of any generalized Witt algebra
, with the right kernel of being , are explicitly described; the isomorphisms between any two simple generalized Witt algebras are completely determined; and the second cohomology group for any simple generalized Witt algebra is computed. The derivations, the automorphisms and the second cohomology groups of some special generalized Witt algebras have been studied by several other authors as indicated in the references.

     

Waveguide arrays in selectively infiltrated photonic crystal fibres

The periodic array of air holes in the cladding of a photonic crystal fibre (PCF) provides a convenient scaffold for the introduction of an infiltrating liquid. In this paper we demonstrate a novel platform of one-dimensional tuneable nonlinear photonic lattices produced by selectively infiltrating a row of holes in a PCF. Such structures have been realised by blocking individual holes on one end of a PCF, leaving the desired infiltration pattern unblocked. Unblocked holes are then infiltrated by immersing the unblocked end of the fibre in a reservoir of the infiltrating liquid, allowing for the realisation of a wide variety of periodic structures. Such structures are studied for traditional linear and nonlinear effects in periodic systems.     

An Efficient Implementation of High-Order Coupled-Cluster Techniques Applied to Quantum Magnets

We illustrate how the systematic inclusion of multi-spin correlations of the quantum spin–lattice systems can be efficiently implemented within the framework of the coupled-cluster method by examining the ground-state properties of both the square-lattice and the frustrated triangular-lattice quantum antiferromagnets. The ground-state energy and the sublattice magnetization are calculated for the square-lattice and triangular-lattice Heisenberg antiferromagnets, and our best estimates give values for the sublattice magnetization which are 62% and 51% of the classical results for the square and triangular lattices, respectively. We furthermore make a conjecture as to why previous series expansion calculations have not indicated Néel-like long-range order for the triangular-lattice Heisenberg antiferromagnet. We investigate the critical behavior of the anisotropic systems by obtaining approximate values for the positions of phase transition points.     

Non-coplanar Model States in Quantum Magnetism Applications of the High-Order Coupled Cluster Method

Journal of Statistical Physics - Coplanar model states for applications of the coupled cluster method (CCM) to problems in quantum magnetism are those in which all spins lie in a plane, whereas...