Operators that admit a moment sequence

We consider the question of which operators on Hilbert space admit a moment sequence, and show, in particular, that ifT is any operator inL(itH) that can be written asT=N+K, whereN is normal andK is compact, andM⊂itH is any invariant subspace forT, then the restrictionT/itM admits such a sequence.     

Characterization of SDP Designs That Yield Certain Spin Models

We characterize the SDP designs that give rise to four-weight spin models with two values. We prove that the only such designs are the symplectic SDP designs. The proof involves analysis of the cardinalities of intersections of four blocks.AMS classification:05B20, 05E30     

Crossed-coil detection of two-photon excited nuclear quadrupole resonance

Applying a recently developed theoretical framework for determining two-photon excitation Hamiltonians using average Hamiltonian theory, we calculate the excitation produced by half-resonant irradiation of the pure quadrupole resonance of a spin-3/2 system. This formalism provides expressions for the single-quantum and double-quantum mutation frequencies as well as the Bloch-Siegert shift. The dependence of the excitation strength on RF field orientation and the appearance of the free-induction signal along an axis perpendicular to the excitation field provide an unmistakable signature of two-photon excitation. We demonstrate single- and double-quantum excitation in an axially symmetric system using 35Cl in a single crystal of potassium chlorate (omega(Q) = 28 MHz) with crossed-coil detection. A rotation plot verifies the orientation dependence of the two-photon excitation, and double-quantum coherences are observed directly with the application of a static external magnetic field.     

In situ reactivity and FTIR study of the wet and dry photooxidation of propane on anatase TiO2

The photocatalytic oxidation (PCO) of trace amounts of propane (500 ppm) on nanocrystalline anatase TiO2 has been investigated in situ as a function of temperature (T = 318-473 K), humidity (C(H2O) = 0-4%), and time by means of mass spectrometry and diffuse reflectance Fourier transform infrared spectroscopy (DRIFT). Propane adsorbs associatively on TiO2 at 318 K in dry air, while at 473 K small amounts of thermal dissociation products appear on the surface. In agreement with previous studies, propane is found primarily to be converted to acetone by reactions with photogenerated oxygen radicals. Various successive reaction paths exist, where the branching depends on the temperature and hydroxylation state of the surface. Under dry conditions at 318 K, acetone oxidation is initially kinetically hindered, while, above 400 K, acetone readily decomposes. The thermally assisted reaction channel leads to detrimental bonding of surface species and inhibition of the catalytic activity. It is manifested by a coloration of the sample and suggested to be coupled to surface reduction. Under humidified conditions, there is an optimum of the PCO in C(H2O) and T space, which is estimated to correspond to an equilibrium coverage of one monolayer of H2O (or bilayer). The latter reaction condition also corresponds to sustained high propane conversion and is characterized by rapid establishment of steady state rates. The optimum PCO is discussed in terms of a balance between (i) sustaining enough of a photoactive water monolayer to avoid detrimental bonding of surface species, (ii) allowing reactants to adsorb and access bulk TiO2 photoexcitations, and at the same time (iii) maximizing the thermally assisted decomposition of intermediates.     

Effect of NO upon N2O decomposition over Fe/ZSM-5 with low iron loading

An Fe/ZSM-5 catalyst with a very high Si/Al ratio was prepared, and using it, the effect of NO upon the kinetics of N2O decomposition was studied. The addition of small, nonstoichiometric amounts of NO was observed to cause the rate to increase by more than an order of magnitude. The kinetics were well-fit by a rate expression that was first order in the partial pressure of N2O for the situation without added NO and separately for the situation where NO was added. The Arrhenius parameters of the rate coefficient differed for the two situations. The results are consistent with a mechanistic scheme wherein the reaction proceeds via an oxide-oxo redox cycle in the absence of NO. The results suggest that the NO-assisted decomposition of N2O does not require a second iron site adjacent to the active site and that NOx species adsorbed on the same cation site could serve as locations for oxygen storage if, in fact, the promotional effect of NO is related to such storage.     

Identification of lipid aggregate structures on TiO2 surface using headgroup IR bands

Attenuated total reflection-Fourier transform infrared (ATR-FTIR) spectroscopy was used to study the nature of the dipalmitoylphosphatidylcholine (DPPC) aggregated structures adsorbed on TiO(2). DPPC molecules were assembled on TiO(2) using Langmuir-Blodgett (LB) deposition methods or by directly flowing the DPPC liposome solution across the TiO(2)-coated ATR crystal. We found that there is a direct correlation between the intensity and frequency position of the zwitterionic headgroup IR bands and the nature of LB films. Specifically, we have shown that the bands due to PO(2)(-) modes are sensitive to changes in the degree of hydration of the LB films and that the symmetric deformation vibrational mode (delta(s) (+)N-CH(3)) is sensitive to interaction with oppositely charged surface sites. Using this information, we found that the liposomes adsorbed on TiO(2) remain intact as vesicles and that the vesicles are stable and not removed in flowing water. We have also shown that the antisymmetric deformation vibrational (delta(as) (+)N-CH(3)) modes are sensitive to changes in lateral-lateral DPPC interactions. This information was used to show that there is a lateral interaction between each positively charged (+)N(CH(3))(3) headgroup and negatively charged PO(2)(-) headgroup of the adjacent DPPC molecule in the adsorbed vesicles and LB films. This study provides a framework for the use of this IR technique in studies of adsorption and transport of molecules across membrane interfaces.     

Ghost busting: Making sense of non-Hermitian Hamiltonians

The Lee model is an elementary quantum field theory in which mass, wave-function, and charge renormalization can be performed exactly. In early studies of this model in the 1950's it was found that there is a critical value of g ², the square of the renormalized coupling constant, above which g ₀ ² , the square of the unrenormalized coupling constant, is negative. For g ² larger than this critical value, the Hamiltonian of the Lee model becomes non-Hermitian. In this non-Hermitian regime a new state appears whose norm is negative. This state is called a ghost. It has always been thought that in this ghost regime the Lee model is an unacceptable quantum theory because unitarity appears to be violated. However, in this regime while the Hamiltonian is not Hermitian, it does possess symmetry. It has recently been discovered that a non-Hermitian Hamiltonian having symmetry may define a quantum theory that is unitary. The proof of unitarity requires the construction of a time-independent operator called C. In terms of C one can define a new inner product with respect to which the norms of the states in the Hilbert space are positive. Furthermore, it has been shown that time evolution in such a theory is unitary. In this talk the C operator for the Lee model in the ghost regime is constructed in the V/Nθ sector. It is then shown that the ghost state has a positive norm and that the Lee model is an acceptable unitary quantum field theory for all values of g ². Presented at the 3rd International Workshop “Pseudo-Hermitian Hamiltonians in Quantum Physics”, Istanbul, Turkey, June 20–22, 2005.     

Monodisperse poly(triacetylene) oligomers extending from monomer to hexadecamer: joint experimental and theoretical investigation of physical properties

A series of monodisperse Et3-Si-end-capped poly(triacetylene) (PTA) oligomers ranging from monomer to hexadecamer was prepared by a fast and efficient statistical deprotection-oxidative Hay oligomerization protocol. The PTA oligomers exhibit an increasingly deep-yellow color with lengthening of the pi-conjugated backbone, feature excellent solubility in aprotic solvents, and exhibit melting points up to > 22 degrees C for the hexadecameric rod. This new dramatically extended oligo(enediyne) series now enables to investigate the evolution of the physico-chemical effects in PTAs beyond the linear 1/n versus property regime into the higher oligomer region where saturation becomes apparent. We report the results of joint experimental and theoretical studies, including analysis of the 13C NMR spectra, evaluation of the linear (UV/ Vis) and nonlinear [third-harmonic generation (THG) and degenerate four-wave mixing (DFWM)] optical properties, and characterization of the redox properties with cyclic and steady-state voltammetry. Up to the hexadecameric rod, an increasingly facile one-electron reduction step is observed, showing at the stage of the dodecamer, a leveling off tendency from the linear correlation between the inverse number of monomer units and the first reduction potential. The effective conjugation length (ECL) determined by means of UV/Vis spectroscopy revealed a pi-electron-delocalization length of about n = 10 monomeric units, which corroborates well with the oligomeric length for which in the 13C NMR spectrum C(sp2) and C(sp) resonances start to overlap. Third-harmonic generation (THG) and degenerate four-wave mixing (DFWM) measurements revealed for the second-order hyperpolarizability gamma a power law increase gammma-alpha-n(a) for oligomers up to the octamer with exponential factors a= 2.46+/-0.10 and a=2.64+/-0.20, respectively, followed by a smooth saturation around n = 10 repeating units. The power law coefficient a calculated with the help of the valence effective Hamiltonian (VEH) method combined to a sum-over-states (SOS) formalism corroborates well with the values found by both THG and DFWM experiments. Up to the PTA heptamer, INDO (intermediate neglect of differential overlap)-calculated gas-phase ionization potentials and electron affinities obey a linear relationship as a function of the inverse number of monomer units displaying a strong electron-hole symmetry. The onset of saturation for the electron affinity is calculated to occur around the octamer, in accordance with experimentally obtained results from electrochemical measurements.     

Polynomial Interpolation to Data on Flats in

Stimulated by recent work of Hakopian and Sahakian, polynomial interpolation to data at all the s-dimensional intersections of an arbitrary sequence of hyperplanes in ^d is considered, and reduced, by the adjunction of an additional s hyperplanes in general position with respect to the given sequence, to the case s=0 solved much earlier by two of the present authors. In particular, interpolation is from the very same polynomial spaces already used earlier. The difficult question of multiplicity and corresponding matching of derivative information is completely solved, with the number of independent derivative conditions at an intersection exactly equal to that intersection's multiplicity. Also, the consistency requirements placed on the data are minimal in the sense that they need to be checked only at the finitely many 0-dimensional intersections of the hyperplanes involved. The arguments used provide, incidentally, further insights into the two polynomial spaces, (Ξ) and (Ξ), of basic interest in box spline theory.