Chris Barnett

Activation energies for the rate-limiting step in water photooxidation by nanostructured α-Fe2O3 and TiO2.

Competition between charge recombination and the forward reactions required for water splitting limits the efficiency of metal-oxide photocatalysts. A key requirement for the photochemical oxidation of water on both nanostructured α-Fe(2)O(3) and TiO(2) is the generation of photoholes with lifetimes on the order of milliseconds to seconds. Here we use transient absorption spectroscopy to directly probe the long-lived holes on both nc-TiO(2) and α-Fe(2)O(3) in complete PEC cells, and we investigate the factors controlling this slow hole decay, which can be described as the rate-limiting step in water oxidation. In both cases this rate-limiting step is tentatively assigned to the hole transfer from the metal oxide to a surface-bound water species. We demonstrate that one reason for the slow hole transfer on α-Fe(2)O(3) is the presence of a significant thermal barrier, the magnitude of which is found to be independent of the applied bias at the potentials examined. This is in contrast to nanocrystalline nc-TiO(2), where no distinct thermal barrier to hole transfer is observed.

The Itô-Clifford integral

Abstract We present a theory of non-commutative stochastic integration analogous to the Ito-theory. It is shown that Wick products of Fermi fields define martingales and that stochastic integrals with respect to these are defined for adapted (operatorvalued) square-integrable integrands. For square-integrable martingales associated with an arbitrary probability gage space a stochastic integral is defined, and a Doob-Meyer decomposition for supermartingales obtained.

Protein adsorption on nanoporous TiO2 films: a novel approach to studying photoinduced protein/electrode transfer reactions

We have investigated the use of nanoporous TiO2 films as substrates for protein immobilisation. Such films are of interest due to their high surface area, optical transparency, electrochemical activity and ease of fabrication. These films moreover allow detailed spectroscopic study of protein/electrode electron transfer processes. We find that protein immobilisation on such films may be readily achieved from aqueous solutions at 4 degrees C with a high binding stability and no detectable protein denaturation. The nanoporous structure of the film greatly enhances the active surface area available for protein binding (by a factor of up to 850 for an 8 microns thick film). We demonstrate that the redox state of proteins such as immobilised cytochrome-c (Cyt-c) and haemoglobin (Hb) may be modulated by the application of an electrical bias potential to the TiO2 film, without the addition of electron transfer mediators. The binding of Cyt-c on the TiO2 films is investigated as a function of film thickness, protein concentration, protein surface charge and ionic strength. We demonstrate the potential use of immobilised Hb on such TiO2 films for the detection of dissolved CO in aqueous solutions. We further show that protein/electrode electron transfer may be initiated by UV bandgap excitation of the TiO2 electrode. Both photooxidation and photoreduction of the immobilised proteins can be achieved. By employing pulsed UV laser excitation, the interfacial electron transfer kinetics can be monitored by transient optical spectroscopy, providing a novel probe of protein/electrode electron transfer kinetics. We conclude that nanoporous TiO2 films may be useful both for basic studies of protein/electrode interactions and for the development of novel bioanalytical devices such as biosensors.

Quasi-free quantum stochastic integrals for the CAR and CCR

Abstract A theory of quantum martingales and quantum stochastic integrals in quasi-free representations of the CAR and CCR is presented. For the CAR, the results generalize some of those developed in Barnett, Streater, and Wilde ( J. Funct. Anal. 48 (1982), 172–212, J. London Math. Soc. 27 (1983), 373–384) and for the CCR, the results contain the standard Ito theory of stochastic integration with respect to Brownian motion as a special case.

Risk Capital Allocation and Cooperative Pricing of Insurance Liabilities

The Aumann–Shapley [Values of Non-atomic Games, Princeton University Press, Princeton] value, originating in cooperative game theory, is used for the allocation of risk capital to portfolios of pooled liabilities, as proposed by Denault [Coherent allocation of risk capital, J. Risk 4 (1) (2001) 1]. We obtain an explicit formula for the Aumann–Shapley value, when the risk measure is given by a distortion premium principle [Axiomatic characterisation of insurance prices, Insur. Math. Econ. 21 (2) (1997) 173]. The capital allocated to each instrument or (sub)portfolio is given as its expected value under a change of probability measure. Motivated by Mirman and Tauman [Demand compatible equitable cost sharing prices, Math. Oper. Res. 7 (1) (1982) 40], we discuss the role of Aumann–Shapley prices in an equilibrium context and present a simple numerical example.

5–20 keV laser-induced x-ray generation at 1 kHz from a liquid-jet target

We report ultrashort pulse, 1 kHz repetition rate x-ray generation in the 5–20 keV spectral region, induced by the interaction of laser radiation with copper nitrate solution and ethylene glycol liquid-jet targets. The characteristics of the copper nitrate source are relevant for application to time-resolved x-ray diffraction studies as well as for spectroscopic x-ray absorption studies. The x-ray sources were operated uninterrupted for in excess of 5 h with no detectable buildup of debris on the associated optics. The x-ray flux generated by both sources is estimated to be of the order of 106 photons s−1 sr−1 in the 5–20 keV region. The spectra have been measured with both a PIN photodiode, and with transmission measurements taken using aluminum filters. We find that the plasma emission has a broadband component attributed to bremsstrahlung emission, with the bulk of the x-ray emission emitted from the chamber lying between 5 and 20 keV for both sources. The copper nitrate emission, however, delivers a d...

Direct identification and decongestion of Fermi resonances by control of pulse time ordering in two-dimensional IR spectroscopy

We show that it is possible to both directly measure and directly calculate Fermi resonance couplings in benzene. The measurement method used was a particular form of two-dimensional infrared spectroscopy (2D-IR) known as doubly vibrationally enhanced four wave mixing. By using different pulse orderings, vibrational cross peaks could be measured either purely at the frequencies of the base vibrational states or split by the coupling energy. This capability is a feature currently unique to this particular form of 2D-IR and can be helpful in the decongestion of complex spectra. Five cross peaks of the ring breathing mode nu13 with a range of combination bands were observed spanning a region of 1500-4550 cm(-1). The coupling energy was measured for two dominant states of the nu13+nu16 Fermi resonance tetrad. Dephasing rates were measured in the time domain for nu13 and the two (nu13+nu16) Fermi resonance states. The electronic and mechanical vibrational anharmonic coefficients were calculated to second and third orders, respectively, giving information on relative intensities of the cross peaks and enabling the Fermi resonance states of the combination band nu13+nu16 at 3050-3100 cm(-1) to be calculated. The excellent agreement between calculated and measured spectral intensities and line shapes suggests that assignment of spectral features from ab initio calculations is both viable and practicable for this form of spectroscopy.

Stopping non-commutative processes

Stopping times are a powerful tool in the theory of stochastic processes, so it is natural to ask whether they have a counterpart in the theory of non-commutative processes. This paper is a part answer to that question. We show that the ‘ formalism ’ of stopping times carries over to a non-commutative context and prove an Optional Stopping Theorem.

RANDOM TIMES AND TIME PROJECTIONS

Random times and their associated time projections are discussed within the context of quantum probability theory. A stochastic integral repre- sentation for time projections is obtained, and their order structure is investi- gated. A quantum analogue of the classical result relating the range and bounded stoppings of the stochastic integral is proved.

A non-commutative random stopping theorem

Abstract A theory of non-commutative stopping time is presented in the case where the underlying Von Neumann algebra possesses only a faithful normal state. In particular we prove an analogue of Doobs optional stopping theorem and in the special case of the quasi-free representation of the CAR we are also able to prove the random stopping theorem. These results thus extend those established by C. Barnett and T. J. Lyons (1985, Math. Proc. Cambridge Philos. Soc. ) to include certain type III factors.