Boson pairs in a one-dimensional split trap

We describe the properties of a pair of ultracold bosonic atoms in a one-dimensional harmonic trapping potential with a tunable zero-ranged barrier at the trap center. The full characterization of the ground state is done by calculating the reduced single-particle density, the momentum distribution, and the two-particle entanglement. We derive several analytical expressions in the limit of infinite repulsion (Tonks-Girardeau limit) and extend the treatment to finite interparticle interactions by numerical solution. As pair interactions in double wells form a fundamental building block for many-body systems in periodic potentials, our results have implications for a wide range of problems.

‘Towards a Green New Deal on the Island of Ireland: from economic crisis to a new political economy of sustainability’

This article begins from the assumption (which may seem controversial to many) that anyone who thinks that our current economic crisis is a temporary blip until ‘normal service’ (i.e. a return to ‘business as usual’) is resumed, profoundly misunderstands the severity and significance of what’s happening to the global economy and its impacts on the future prosperity of the island of Ireland. The economic recession represents nothing short of a re-structuring of the global economy and the creation of a new dispensation between governments, markets and citizens. The full implications of the re-regulation of the market, with the state bailing out and part nationalising the financial sector in both jurisdictions on the island (as in other parts of the world) have yet to be seen, but what we are witnessing is the emergence of a new economic model. Those who think we can, or even ought to, return to the pre-2008 economic model, are gravely mistaken. The current economic downturn marks the end of the ‘neo-liberal’ model and the beginnings of the transition (an inevitable transition, this article will argue) towards a new low carbon, renewable, green and sustainable economy and society.

Sequential C-H and C-Ru bond formation and cleavage during the thermally induced rearrangement of aryl ruthenium(II) complexes with [C6H3(CH2NMe2)(2)-2,6](-) as a bidentate eta(2)-C,N coordinated ligand. The crystal structures of the isomeric pairs [RuCl{eta(6)-C10H14}{eta(2)-C,N-C6H3(CH2NMe2)(2)-2,n}] (n = 4 or 6) and [Ru(eta(5)-C5H5){(eta(2)-C,N-C6H3(CH2NMe2)(2)-2,n} (PPH3)] (n = 4 or 6)

New air-stable ruthenium(II) complexes that contain the aryldiamine ligand [C6H3(CH2-NMe2)(2)-2,6](-) (NCN) are described. These complexes are [RuCl{eta(2)-C,N-C6H3(CH2NMe2)(2)-2,6}(eta(6)-C10H14)] (2; C10H14 = p-cymene = C6H4Me-Pr-i-4), [Ru{eta(2)-C,N-C6H3(CH2NMe2)(2)-2,6}(eta(5)-C5H5)(PPh3)] (5), and their isomeric forms [RuCl{eta(2)-C,N-C6H3(CH2NMe2)(2)-2,4}(eta(6)-C10H14)] (3) and [Ru{eta(2)-C,N-C6H3(CH2NMe2)(2)-2,4}(eta(5)-C5H5)(PPh3)] (6), respectively. Complex 2 has been prepared from the reaction of [Li(NCN)](2) with [RuCl2(eta(6)-C10H14)](2), whereas complex 5 has been prepared by the treatment of [RuCl{eta(3)-N,C,N-C6H3(CH2NMe2)(2)-2,6}(PPh3)] (4) with [Na(C5H5)](n). Both 2 and 5 are formally 18-electron ruthenium(II) complexes in which the monoanionic potentially tridentate coordinating ligand NCN is eta(2)-C,N-bonded, In solution (halocarbon solvent at room temperature or in aromatic solvents at elevated temperature), the intramolecular rearrangements of 2 and 5 afford complexes 3 and 6, respectively. This is a result of a shift of the metal-C-aryl bond from position-1 to position-3 on the aromatic ring of the NCN ligand. The mechanism of the isomerization is proposed to involve a sequence of intramolecular oxidative addition and reductive elimination reactions of both aromatic and aliphatic C-H bonds. This is based on results from deuterium labeling, spectroscopic studies, and some kinetic experiments. The mechanism is proposed to contain fully reversible steps in the case of 5, but a nonreversible step involving oxidative addition of a methyl NCH2-H bond in the case of 2. The solid-state structures of complexes 2, 3, 5, and 6 have been determined by single-crystal X-ray diffraction. A new dinuclear 1,4-phenylene-bridged bisruthenium(II) complex, [1,4-{RuCl(eta(6)-C10H14)}(2){C-6(CH2NMe2)(4)-2,3,5,6-C,N,C',N'}] (9) has also been prepared from the dianionic ligand [C-6(CH2NMe2)(4)-2,3,5,6](2-) (C2N4). The C2N4 ligand is in an eta(2)-C,N-eta(2)-C',N'-bis(bidentate) bonding mode. Compound 9 does not isomerize in solution (halocarbon solvent), presumably because of the absence of an accessible C-aryl-H bond. Complex 9 could not be isolated in an analytically pure form, probably because of its high sensitivity to air and very low solubility, which precludes recrystallization.