The solvation and redox behavior of mixed ligand copper(II) complexes of acetylacetonate and aromatic diimines in ionic liquids

The behavior of two cationic copper complexes of acetylacetonate and 2,2'-bipyridine or 1,10-phenanthroline, [Cu(acac)(bipy)]Cl (1) and [Cu(acac)(phen)]Cl (2), in organic solvents and ionic liquids, was studied by spectroscopic and electrochemical techniques. Both complexes showed solvatochromism in ionic liquids although no correlation with solvent parameters could be obtained. By EPR spectroscopy rhombic spectra with well-resolved superhyperfine structure were obtained in most ionic liquids. The spin Hamiltonian parameters suggest a square pyramidal geometry with coordination of the ionic liquid anion. The redox properties of the complexes were investigated by cyclic voltammetry at a Pt electrode (d = 1 mm) in bmimBF(4) and bmimNTf(2) ionic liquids. Both complexes 1 and 2 are electrochemically reduced in these ionic media at more negative potentials than when using organic solvents. This is in agreement with the EPR characterization, which shows lower A(z) and higher g(z) values for the complexes dissolved in ionic liquids, than in organic solvents, due to higher electron density at the copper center. The anion basicity order obtained by EPR is NTf2-, N(CN)(2)(-), MeSO4- and Me2PO4-, which agrees with previous determinations. (C) 2013 Elsevier B.V. All rights reserved

The solvation and electrochemical behavior of copper acetylacetonate complexes in ionic liquids

The behavior of copper(II) complexes of pentane-2,4-dione and 1,1,1,5,5,5-hexafluoro-2,4-pentanedione, [Cu(acac)(2) (1) and [Cu(HFacac)(2)(H2O)] (2), in ionic liquids and molecular organic solvents, was studied by spectroscopic and electrochemical techniques. The electron paramagnetic resonance characterization (EPR) showed well-resolved spectra in most solvents. In general the EPR spectra of [Cu(acac)(2)] show higher g(z) values and lower hyperfine coupling constants, A(z), in ionic liquids than in organic solvents, in agreement with longer Cu-O bond lengths and higher electron charge in the copper ion in the ionic liquids, suggesting coordination of the ionic liquid anions. For [Cu(HFacac)(2)(H2O)] the opposite was observed suggesting that in ionic liquids there is no coordination of the anions and that the complex is tetrahedrically distorted. The redox properties of the Cu(II) complexes were investigated by cyclic voltammetry (CV) at a Pt electrode (d = 1 mm), in bmimBF(4) and bmimNTf(2) ionic liquids and, for comparative purposes, in neat organic solvents. The neutral copper(II) complexes undergo irreversible reductions to Cu(I) and Cu(0) species in both ILs and common organic solvents (CH2Cl2 or acetonitrile), but, in ILs, they are usually more easier to reduce (less cathodic reduction potential) than in the organic solvents. Moreover, 1 and 2 are easier to reduce in bmimNTf(2) than in bmimBF(4) ionic liquid. (C) 2013 Elsevier B.V. All rights reserved

Cartan subalgebras in C*-algebras of Hausdorff etale groupoids

The reduced $C^*$-algebra of the interior of the isotropy in any Hausdorff \'etale groupoid $G$ embeds as a $C^*$-subalgebra $M$ of the reduced $C^*$-algebra of $G$. We prove that the set of pure states of $M$ with unique extension is dense, and deduce that any representation of the reduced $C^*$-algebra of $G$ that is injective on $M$ is faithful. We prove that there is a conditional expectation from the reduced $C^*$-algebra of $G$ onto $M$ if and only if the interior of the isotropy in $G$ is closed. Using this, we prove that when the interior of the isotropy is abelian and closed, $M$ is a Cartan subalgebra. We prove that for a large class of groupoids $G$ with abelian isotropy---including all Deaconu--Renault groupoids associated to discrete abelian groups---$M$ is a maximal abelian subalgebra. In the specific case of $k$-graph groupoids, we deduce that $M$ is always maximal abelian, but show by example that it is not always Cartan.Comment: 14 pages. v2: Theorem 3.1 in v1 incorrect (thanks to A. Kumjain for pointing out the error); v2 shows there is a conditional expectation onto $M$ iff the interior of the isotropy is closed. v3: Material (including some theorem statements) rearranged and shortened. Lemma~3.5 of v2 removed. This version published in Integral Equations and Operator Theor

Unitarity of Quantum Theory and Closed Time-Like Curves

Interacting quantum fields on spacetimes containing regions of closed timelike curves (CTCs) are subject to a non-unitary evolution $X$. Recently, a prescription has been proposed, which restores unitarity of the evolution by modifying the inner product on the final Hilbert space. We give a rigorous description of this proposal and note an operational problem which arises when one considers the composition of two or more non-unitary evolutions. We propose an alternative method by which unitarity of the evolution may be regained, by extending $X$ to a unitary evolution on a larger (possibly indefinite) inner product space. The proposal removes the ambiguity noted by Jacobson in assigning expectation values to observables localised in regions spacelike separated from the CTC region. We comment on the physical significance of the possible indefiniteness of the inner product introduced in our proposal.Comment: 13 pages, LaTeX. Final revised paper to be published in Phys Rev D. Some changes are made to expand our discussion of Anderson's Proposal for restoring unitarit

A new dynamical reflection algebra and related quantum integrable systems

We propose a new dynamical reflection algebra, distinct from the previous dynamical boundary algebra and semi-dynamical reflection algebra. The associated Yang-Baxter equations, coactions, fusions, and commuting traces are derived. Explicit examples are given and quantum integrable Hamiltonians are constructed. They exhibit features similar to the Ruijsenaars-Schneider Hamiltonians.Comment: 16 pages v2: signs in the classical reflection algebra correcte

Active Brownian Particles. From Individual to Collective Stochastic Dynamics

We review theoretical models of individual motility as well as collective dynamics and pattern formation of active particles. We focus on simple models of active dynamics with a particular emphasis on nonlinear and stochastic dynamics of such self-propelled entities in the framework of statistical mechanics. Examples of such active units in complex physico-chemical and biological systems are chemically powered nano-rods, localized patterns in reaction-diffusion system, motile cells or macroscopic animals. Based on the description of individual motion of point-like active particles by stochastic differential equations, we discuss different velocity-dependent friction functions, the impact of various types of fluctuations and calculate characteristic observables such as stationary velocity distributions or diffusion coefficients. Finally, we consider not only the free and confined individual active dynamics but also different types of interaction between active particles. The resulting collective dynamical behavior of large assemblies and aggregates of active units is discussed and an overview over some recent results on spatiotemporal pattern formation in such systems is given.Comment: 161 pages, Review, Eur Phys J Special-Topics, accepte

Measurement of Bottom versus Charm as a Function of Transverse Momentum with Electron-Hadron Correlations in p+p Collisions at sqrt(s)=200 GeV

The momentum distribution of electrons from semi-leptonic decays of charm and bottom for mid-rapidity |y|<0.35 in p+p collisions at sqrt(s)=200 GeV is measured by the PHENIX experiment at the Relativistic Heavy Ion Collider (RHIC) over the transverse momentum range 2 < p_T < 7 GeV/c. The ratio of the yield of electrons from bottom to that from charm is presented. The ratio is determined using partial D/D^bar --> e^{+/-} K^{-/+} X (K unidentified) reconstruction. It is found that the yield of electrons from bottom becomes significant above 4 GeV/c in p_T. A fixed-order-plus-next-to-leading-log (FONLL) perturbative quantum chromodynamics (pQCD) calculation agrees with the data within the theoretical and experimental uncertainties. The extracted total bottom production cross section at this energy is \sigma_{b\b^bar}= 3.2 ^{+1.2}_{-1.1}(stat) ^{+1.4}_{-1.3}(syst) micro b.Comment: 432 authors, 6 pages text, 3 figures. Submitted to Phys. Rev. Lett. Plain text data tables for the points plotted in figures for this and previous PHENIX publications are (or will be) publicly available at http://www.phenix.bnl.gov/papers.htm