Direct Images,Fields of Hilbert Spaces,and Geometric Quantization

Geometric quantization often produces not one Hilbert space to represent the quantum states of a classical system but a whole family H _s of Hilbert spaces, and the question arises if the spaces H _s are canonically isomorphic. Axelrod et al. (J. Diff. Geo. 33:787–902, 1991) and Hitchin (Commun. Math. Phys. 131:347–380, 1990) suggest viewing H _s as fibers of a Hilbert bundle H, introduce a connection on H, and use parallel transport to identify different fibers. Here we explore to what extent this can be done. First we introduce the notion of smooth and analytic fields of Hilbert spaces, and prove that if an analytic field over a simply connected base is flat, then it corresponds to a Hermitian Hilbert bundle with a flat connection and path independent parallel transport. Second we address a general direct image problem in complex geometry: pushing forward a Hermitian holomorphic vector bundle ${E \to Y}$ along a non–proper map ${Y \to S}$ . We give criteria for the direct image to be a smooth field of Hilbert spaces. Third we consider quantizing an analytic Riemannian manifold M by endowing TM with the family of adapted Kähler structures from Lempert and Sz?ke (Bull. Lond. Math. Soc. 44:367–374, 2012). This leads to a direct image problem. When M is homogeneous, we prove the direct image is an analytic field of Hilbert spaces. For certain such M—but not all—the direct image is even flat; which means that in those cases quantization is unique.     

A model of solidification under microgravity conditions

The influence of the microgravity environment on solidification processes is discussed. A simple model of the solidification of a binary-alloy is presented with the chemical diffusion influenced by the gravitational field. Using the results of Mullins and Sekerka, we employ the linear theory of hydrodynamic stability to investigate the interfacial instability driving the pattern-forming processes in solidification. As a result, we estimate the characteristic size of the elements of the emerging pattern. We show that, in spite of good agreement of our result with the size of cellulae observed in experiments, the model cannot explain the changes in the patterns occurring in space environment. In conclusion we shortly discuss the possibility of adding realism to our simple model by including the effect of convection.     

CO2-laser annealing of Al/a-Si:H contact

The paper concerns the possibility of using CW (continuous wave) CO₂-laser annealing (=10.6 m,P 100 W/cm²) for formation of a barrier in the Al/a-Si:H/SS (SS-stainless steel) structures with good rectifyingI–V characteristics. The infrared absorption spectra, photoelectric properties, temperature effect on the conductivity and saturation current were analyzed and various contact models are discussed.We thank P. imanec for useful and stimulating discussion, J. Stuchlík for kindly manufacturing the a-Si:H films for us and D. N. Goncharov for the aid with the measurement of the conductivity temperature dependences.     

Fluorescence staining of yeast cells permeabilized by killer toxin K1: Determination of optimum conditions

Optimal assay conditions were established for the previously described method used to determine the activity ofSaccharomyces cerevisiae pore-forming killer toxin K1. The method is based on cell staining with bromocresol purple. Sensitive cells ofS. cerevisiae from the early exponential phase under nongrowth conditions and in the presence of glucose were the most convenient for determining the killer toxin activity. Maximum killing war reached when the suspension was buffered with 10 mM citrate-phosphate at pH 4.6.     

Critical behavior of self-avoiding walks on fractals

Using a new graph counting technique suitable for self-similar fractals, exact 18th-order series expansions for SAWs on some Sierpinski carpets are generated. From them, the critical fugacityx _c and critical exponents _SAW and _SAW are obtained. The results show a linear dependence of the critical fugacity with the average number of bonds per site of the lattices studied. We find for some carpets with low lacunarity that _SAW<0.75, thus violating the relation _SAW(fractal) > _SAW (d) for SAWs on the fractals which are embedded in ad-dimensional Euclidean space.