A terminal molybdenum carbide prepared by methylidyne deprotonation

The carbide anion [CMo{N(R)Ar}_3]– [R = C(CD_3)_2CH_3, Ar = C_6H_3Me_2-3,5], is obtained by deprotonation of the corresponding methylidyne compound, [HCMo{N(R)Ar}_3], and is characterized by X-ray diffraction as its {K(benzo-15-crown-5)_2}+ salt, thereby providing precedent for the carbon atom as a terminal substituent in transition-metal chemistry

Generating-function method for fusion rules

This is the second of two articles devoted to an exposition of the generating-function method for computing fusion rules in affine Lie algebras. The present paper focuses on fusion rules, using the machinery developed for tensor products in the companion article. Although the Kac-Walton algorithm provides a method for constructing a fusion generating function from the corresponding tensor-product generating function, we describe a more powerful approach which starts by first defining the set of fusion elementary couplings from a natural extension of the set of tensor-product elementary couplings. A set of inequalities involving the level are derived from this set using Farkas' lemma. These inequalities, taken in conjunction with the inequalities defining the tensor products, define what we call the fusion basis. Given this basis, the machinery of our previous paper may be applied to construct the fusion generating function. New generating functions for sp(4) and su(4), together with a closed form expression for their threshold levels are presented.Comment: Harvmac (b mode : 47 p) and Pictex; to appear in J. Math. Phy

Generating-function method for tensor products

This is the first of two articles devoted to a exposition of the generating-function method for computing fusion rules in affine Lie algebras. The present paper is entirely devoted to the study of the tensor-product (infinite-level) limit of fusions rules. We start by reviewing Sharp's character method. An alternative approach to the construction of tensor-product generating functions is then presented which overcomes most of the technical difficulties associated with the character method. It is based on the reformulation of the problem of calculating tensor products in terms of the solution of a set of linear and homogeneous Diophantine equations whose elementary solutions represent ``elementary couplings''. Grobner bases provide a tool for generating the complete set of relations between elementary couplings and, most importantly, as an algorithm for specifying a complete, compatible set of ``forbidden couplings''.Comment: Harvmac (b mode : 39 p) and Pictex; this is a substantially reduced version of hep-th/9811113 (with new title); to appear in J. Math. Phy

A precise CNOT gate in the presence of large fabrication induced variations of the exchange interaction strength

We demonstrate how using two-qubit composite rotations a high fidelity controlled-NOT (CNOT) gate can be constructed, even when the strength of the interaction between qubits is not accurately known. We focus on the exchange interaction oscillation in silicon based solid-state architectures with a Heisenberg Hamiltonian. This method easily applies to a general two-qubit Hamiltonian. We show how the robust CNOT gate can achieve a very high fidelity when a single application of the composite rotations is combined with a modest level of Hamiltonian characterisation. Operating the robust CNOT gate in a suitably characterised system means concatenation of the composite pulse is unnecessary, hence reducing operation time, and ensuring the gate operates below the threshold required for fault-tolerant quantum computation.Comment: 9 pages, 8 figure

Radical anionic versus neutral 2,2′-bipyridyl coordination in uranium complexes supported by amide and ketimide ligands

The synthesis and characterization of (bipy)₂U(N[t-Bu]Ar)₂ (1-(bipy)₂, bipy = 2,2′-bipyridyl, Ar = 3,5-C₆H₃Me₂), (bipy)U(N[1Ad]Ar)₃ (2-bipy), (bipy)₂U(NC[t-Bu]Mes)₃ (3-(bipy)2, Mes = 2,4,6-C₆H₂Me₃), and IU(bipy)(NC[t-Bu]Mes)₃ (3-I-bipy) are reported. X-ray crystallography studies indicate that bipy coordinates as a radical anion in 1-(bipy)₂ and 2-bipy, and as a neutral ligand in 3-I-bipy. In 3-(bipy)₂, one of the bipy ligands is best viewed as a radical anion, the other as a neutral ligand. The electronic structure assignments are supported by NMR spectroscopy studies of exchange experiments with 4,4′-dimethyl-2,2′-bipyridyl and also by optical spectroscopy. In all complexes, uranium was assigned a +4 formal oxidation state.National Science Foundation (U.S.) (Grant CHE-9988806

Berenstein-Zelevinsky triangles, elementary couplings and fusion rules

We present a general scheme for describing su(N)_k fusion rules in terms of elementary couplings, using Berenstein-Zelevinsky triangles. A fusion coupling is characterized by its corresponding tensor product coupling (i.e. its Berenstein-Zelevinsky triangle) and the threshold level at which it first appears. We show that a closed expression for this threshold level is encoded in the Berenstein-Zelevinsky triangle and an explicit method to calculate it is presented. In this way a complete solution of su(4)_k fusion rules is obtained.Comment: 14 page