Almost Commuting Unitary Matrices Related to Time Reversal

The behavior of fermionic systems depends on the geometry of the system and the symmetry class of the Hamiltonian and observables. Almost commuting matrices arise from band-projected position observables in such systems. One expects the mathematical behavior of almost commuting Hermitian matrices to depend on two factors. One factor will be the approximate polynomial relations satisfied by the matrices. The other factor is what algebra the matrices are in, either ${{\bf M}_n(\mathbb{A})}$ M n ( A ) for ${\mathbb{A} = \mathbb{R}}$ A = R , ${\mathbb{A} = \mathbb{C}}$ A = C or ${\mathbb{A} = \mathbb{H}}$ A = H , the algebra of quaternions. There are potential obstructions keeping k-tuples of almost commuting operators from being close to a commuting k-tuple.We consider two-dimensional geometries and so this obstruction lives in ${KO_{-2}(\mathbb{A})}$ K O - 2 ( A ) . This obstruction corresponds to either the Chern number or spin Chern number in physics. We show that if this obstruction is the trivial element in K-theory then the approximation by commuting matrices is possible.     

Interpreting single turnover catalysis measurements with constrained mean dwell times

Observation of a chemical transformation at the single-molecule level yields a detailed view of kinetic pathways contributing to the averaged results obtained in a bulk measurement. Studies of a fluorogenic reaction catalyzed by gold nanoparticles have revealed heterogeneous reaction dynamics for these catalysts. Measurements on single nanoparticles yield binary trajectories with stochastic transitions between a dark state in which no product molecules are adsorbed and a fluorescent state in which one product molecule is present. The mean dwell time in either state gives information corresponding to a bulk measurement. Quantifying fluctuations from mean kinetics requires identifying properties of the fluorescence trajectory that are selective in emphasizing certain dynamic processes according to their time scales. We propose the use of constrained mean dwell times, defined as the mean dwell time in a state with the constraint that the immediately preceding dwell time in the other state is, for example, less than a variable time. Calculations of constrained mean dwell times for a kinetic model with dynamic disorder demonstrate that these quantities reveal correlations among dynamic fluctuations at different active sites on a multisite catalyst. Constrained mean dwell times are determined from measurements of single nanoparticle catalysis. The results indicate that dynamical fluctuations at different active sites are correlated, and that especially rapid reaction events produce particularly slowly desorbing product molecules.     

Broad reactivity trends for oxygen-isotope exchange from the near-surface regions of some metal (hydr)oxide solids

The flux of (18)O from suspensions of isotopically enriched Cr(III) and Rh(III) hydroxide solids at varying temperature and pH was measured in a series of experiments. Most of these solids are metal hydroxide nanospheres that have a large surface area and a narrow distribution in particle sizes and contain inert metals (Cr(III) and Rh(III)). Using rate data for dissolved multimeric complexes as a guide, the solids were enriched in (18)O under conditions that were intended to affect mostly bound water molecules (eta-OH(2)) at the surface, but this point could not be verified. Nevertheless, the fluxes of (18)O back into solution from the isotopically enriched surfaces indicate that increased pH, which partly deprotonates the surface, is surprisingly unimportant to the rate and does not measurably affect (18)O fluxes. Although these data are sparse, Rh(III) solids react at rates that are lower than for Cr(III) solids, and the rates of exchange for crystalline and amorphous solids are relatively close. The results indicate that rates of ligand exchange at these surface sites are controlled dominantly by the local metal-oxygen bond strengths and that long-range forces are relatively unimportant. These experiments also indicate a strategy for measuring rates of ligand exchange from solid surfaces.     

Normal Elements of C*-Algebras of Real Rank Zero without Finite-Spectrum Approximants

We investigate inductive limits of Toeplitz-type C*-algebras.One example, which has real-rank zero, is the middle term ofan exact sequence where is a Bunce-Deddens algebra and I is AF. Using Berg's technique,we produce a normal element N that is not the limit of finite-spectrumnormals. Moreover, this is an example of a normal element inan inductive limit that is not the limit of normal elementsof the approximating subalgebras. A second example is an embedding of C() ( the closed disk) into , where is a simple AF algebra and is the Toeplitz algebra.Let _n, for n 2, be the CW complex obtained as the quotientof by an n-fold identification of the boundary. (So ₂ = RP².)Regarding C(_n) as a subalgebra of C(), we find nontrivial embeddingsof C(_n) into type I inductive limits. From this, we producea *-homomorphism, for n odd, C₀(_n\{pt}) _{n + 1}, that inducesan isomorphism on K-theory. More generally, for X a connectedCW complex minus a point, and for n odd, we show that the map is a split surjection.     

C-H-pi interactions in 1-n-butyl-3-methylimidazolium tetraphenylborate molten salt: solid and solution structures

The crystal structure of 1-n-butyl-3-methylimidazolium tetraphenylborate molten salt (1) shows C-H-pi interactions between the hydrogens of the imidazolium cation and the phenyl rings of the tetraphenylborate anion. The imidazolium ring is surrounded by three tetraphenylborate anions that are connected with the same cation by C-H-pi (phenyl rings) interactions. The nearest inter-ion interaction is found between the N-CH-N proton of the cation and the B-phenyl centroid (2.349 A) with a nearly T-shaped geometry. The inter-ionic solution structure of 1 has been investigated by the detection of inter-ionic contacts in 1H NOESY NMR spectra between the protons of the cation and the anion. The 1H-NMR spectra of molten salt 1 is almost independent of its concentration in [D6]DMSO solution, the imidazolium proton chemical shifts are in the expected region and there are no observable NOE effects between the protons of the cation with those of the anion, indicating that 1 behaves in [D6]DMSO as a solvent-separated ion pair. In CDCl3 the 1H-NMR spectra of 1 are concentration dependent and all the imidazolium protons are shielded as compared with those observed in [D6]DMSO. Moreover, the 1H NOESY NMR spectra show all the peaks affected by the interaction between the protons of the imidazolium cation and those of the anion, indicating that in CDCl3 1 possesses a contact ion pair structure. The NCHN proton of the cation exhibits the greatest shielding (up to -4.5 ppm). an indication of the existence of C-H-pi interactions, even in solution. The calculated distance of this proton to the phenyl centroid is 2.3 A for a C-H -pi angle of 180 degrees. The apparent volumes for the cation and anion, calculated from the measured 13C-NMR relaxation times, increase from 38 and 140 A3 in [D6]DMSO to 360 and 600 A3 in CDCl3, respectively; this indicates the formation of floating aggregates of the type (1)(n) in CDCl3 via weak hydrogen bonds, with increasing concentration.     

Effects of Adsorbed Polyaniline on Redox Processes on As(2)O(3) Surfaces

Polyaniline deposited on As(2)O(3) surface resulted in a new material, which was characterized by infrared spectoscopy, thermogravimetry, differential scanning calorimetry, scanning electron microscopy, X-ray diffraction, and cyclic voltammetry. The mass percentage of polymer deposited on oxide surface is approximately 13%. The scanning electron microscopy images as well as the X-ray diffraction patterns provided conclusive evidence that the oxide surface is coated by the polymer. The cyclic voltammograms of the polyaniline adsorbed on As(2)O(3) surface showed that the adsorbate exerts remarkable effects on redox processes on this oxide. The pure oxide exhibited two oxidation/reduction peaks at 0.25/-0.06 and 0.47/-0.25 V attributed tentatively to the processes As(2)O(3)(s)+6H(+)+6e(-)=2As(s)+3H(2)O and As(s)+3H(+)+3e(-)=AsH(3)(g), respectively. The polyaniline-coated sample exhibited a better-defined voltammogram in which the first oxidation peak of the oxide had its intensity increased about four times. Copyright 2000 Academic Press.