Linear spin-zero quantum fields in external gravitational and scalar fields

We give mathematically rigorous results on the quantization of the covariant Klein Gordon field with an external stationary scalar interaction in a stationary curved space-time. We show how, following Segal, Weinless etc., the problem reduces to finding a “one particle structure” for the corresponding classical system. Our main result is an existence theorem for such a one-particle structure for a precisely specified class of stationary space-times. Byproducts of our approach are:

1. A discussion of when a given “equal-time” surface in a given stationary space-time is Cauchy.
2. A modification and extension of the methods of Chernoff [3] for proving the essential self-adjointness of certain partial differential operators.

     

Water adsorption, desorption, and clustering on FeO(111)

The adsorption of water on FeO(111) is investigated using temperature programmed desorption (TPD) and infrared reflection absorption spectroscopy (IRAS). Well-ordered 2 ML thick FeO(111) films are grown epitaxially on a Pt(111) substrate. Water adsorbs molecularly on FeO(111) and desorbs with a well resolved monolayer peak. IRAS measurements as a function of coverage are performed for water deposited at 30 and 135 K. For all coverages (0.2 ML and greater), the adsorbed water exhibits significant hydrogen bonding. Differences in IRAS spectra for water adsorbed at 30 and 135 K are subtle but suggest that water adsorbed at 135 K is well ordered. Monolayer nitrogen TPD spectra from water covered FeO(111) surfaces are used to investigate the clustering of the water as a function of deposition or annealing temperature. Temperature dependent water overlayer structures result from differences in water diffusion rates on bare FeO(111) and on water adsorbed on FeO(111). Features in the nitrogen TPD spectra allow the monolayer wetting and 2-dimensional (2D) ordering of water on FeO(111) to be followed. Voids in a partially disordered first water layer exist for water deposited below 120 K and ordered 2D islands are found when depositing water above 120 K.     

Probing depth of the low energy cascade electrons from a transition metal

A surface probing depth of only 2 layers for low energy cascade electrons excited with a 3.2 keV primary electron beam is clearly demonstrated by model experiments with non-magnetic overlayers of Ta on magnetic substrates of Fe/Ni₈₀Fe₂₀. This result establishes a short probing depth of low energy electrons in transition metals generalizing the previously observed short magnetic probing depth for spin-polarized electrons in ferromagnets. The short probing depth sheds new light on a number of spectroscopic observations on ferromagnetic transition metals, and has important implications concerning surface magnetic properties and scattering processes of hot electrons in transition metals.     

Imaging intrinsic diffusion of bridge-bonded oxygen vacancies on TiO2(110)

We report the first measurements and calculations of the intrinsic mobility of bridge-bonded oxygen (BBO) vacancies on a rutile TiO2(110). The sequences of isothermal (340-420 K) scanning tunneling microscope images show that BBO vacancies migrate along BBO rows. The hopping rate increases exponentially with increasing temperature with an experimental activation energy of 1.15 eV. Density functional theory calculations are in very good agreement giving an energy barrier for hopping of 1.03 eV. Both theory and experiment indicate repulsive interactions between vacancies on a given BBO row.     

Synthesis and stabilizing properties of amphipolar polyelectrolytes

The European Physical Journal E - A series of well-defined amphipolar block, graft and statistical copolymers based on the same polar and non-polar monomers were synthesized and investigated for...     

Muon transfer from ground state deuterium to helium nuclei and its temperature dependence

The energy and time distributions of the decay X-rays of excited, metastable, molecular (dμHe)*-resonances were measured. The comparison of the observed energy spectra with calculated ones suggests that decay from the rotational state J = 1 dominates at the investigated conditions. The muon transfer rates from ground state deuterium to the helium isotopes ³He and ⁴He at low temperatures were determined from the time distributions of these spectra. Additionally, the temperature dependence of the muon transfer rate was clearly established in deuterium / ⁴He mixtures. This revised version was published online in August 2006 with corrections to the Cover Date.     

Journey toward Teaching Mathematics through Problem Solving

Teaching mathematics through problem solving is a challenge for teachers who learned mathematics by doing exercises. How do teachers develop their own problem solving abilities as well as their abilities to teach mathematics through problem solving? A group of teachers began the journey of learning to teach through problem solving while taking a Teaching Elementary School Mathematics graduate course. This course was designed to engage teachers in problem solving during class meetings and required them to do problem solving action research in their classrooms. Although challenged by the course problem solving work, teachers became more comfortable with the mathematics and recognized the importance of group work while problem solving. As they worked with their students, teachers were more confident in their students' abilities to be successful problem solvers. For some teachers, a strong problem solving foundation was established. For others, the foundation was more tentative.     

Tracking regression and progression of atherosclerosis in human carotid arteries using high-resolution magnetic resonance imaging

BACKGROUND AND PURPOSE: Magnetic resonance imaging (MRI) can accurately and reproducibly measure the volume of atherosclerotic plaque in human carotid arteries. Atherosclerotic plaques may either progress or regress over time, depending on individual risk factors and treatment regimens. This study was designed to determine if regression or progression of human carotid atherosclerosis in patients receiving statin therapy over 24 months can be detected by high-resolution MRI. METHODS: In 11 subjects who had undergone unilateral carotid endarterectomy and were on statin therapy, volumes for total carotid artery, concentric wall (normal wall), eccentric wall (plaque), and lumen were quantified at 0, 16 and 24 months using a 1.5-T human imager equipped with 6-cm phased array coils. RESULTS: The interobserver mean coefficient of variation (CV) was lowest for the lumen volume (3.1%) and highest for the plaque volume (9.8%). The interscan mean CV was lowest for the total artery volume (3.2%) and highest for the plaque volume (9.9%). As much as 26% regression and 35% progression were observed in individual subject's carotid artery eccentric wall (plaque) volumes over time. Mean eccentric wall volume increased 5% by 16 months and 8% by 24 months. Mean total wall volume increased slightly at both 16 and 24 months (+1.2% and +1.8%). CONCLUSIONS: High-resolution MRI provides a noninvasive reproducible method of tracking changes in carotid atherosclerosis. This pilot study detected changes in individual subjects at both 16 and 24 months. MRI tracking of changes in atherosclerotic plaques should prove useful in assessing vascular disease risk and monitoring the efficacy of interventions designed to induce regression or retard progression.     

Linear spin-zero quantum fields in external gravitational and scalar fields

The quantum theory of both linear, and interacting fields on curved space-times is discussed. It is argued that generic curved space-time situations force the adoption of the algebraic approach to quantum field theory: and a suitable formalism is presented for handling an arbitrary quasi-free state in an arbitrary globally hyperbolic space-time.For the interacting case, these quasi-free states are taken as suitable starting points, in terms of which expectation values of field operator products may be calculated to arbitrary order in perturbation theory. The formal treatment of interacting fields in perturbation theory is reduced to a treatment of free quantum fields interacting with external sources.Central to the approach is the so-called two-current operator, which characterises the effect of external sources in terms of purely algebraic (i.e. representation free) properties of the source-free theory.The paper ends with a set of Feynman rules which seems particularly appropriate to curved space-times in that it takes care of those aspects of the problem which are specific to curved space-times (and independent of interaction). Heuristically, the scheme calculates in-in rather than in-out matrix elements. Renormalization problems are discussed but not treated.Work partly supported by the Schweizerische Nationalfonds