Singular vectors of the WA2WA_2 algebra

The null vectors of an arbitrary highest weight representation of the $WA_2$ algebra are constructed. Using an extension of the enveloping algebra by allowing complex powers of one of the generators, analysed by Kent for the Virasoro theory, we generate all the singular vectors indicated by the Kac determinant. We prove that the singular vectors with given weights are unique up to normalisation and consider the case when $W_0$ is not diagonalisable among the singular vectors.Comment: 10 pages, LaTeX with 3 figures in LaTe

Null vectors of the WBC2WBC_2 algebra

Using the fusion principle of Bauer et al. we give explicit expressions for some null vectors in the highest weight representations of the \bc algebra in two different forms. These null vectors are the generalization of the Virasoro ones described by Benoit and Saint-Aubin and analogues of the $W_3$ ones constructed by Bowcock and Watts. We find connection between quantum Toda models and the fusion method.Comment: 8 pages, LaTeX, ITP Budapest 50

Testing factorization in B -> D(*)X decays

In QCD the amplitude for B0 -> D(*)+pi- factorizes in the large Nc limit or in the large energy limit Q >> Lambda_QCD where Q = {m_b, m_c, m_b-m_c}. Data also suggests factorization in exclusive processes B-> D* pi+ pi- pi- pi0 and B-> D* omega pi-, however by themselves neither large Nc nor large Q can account for this. Noting that the condition for large energy release in B0-> D+ pi- is enforced by the SV limit, m_b, m_c >> m_b-m_c >> Lambda, we propose that the combined large Nc and SV limits justify factorization in B -> D(*) X. This combined limit is tested with the inclusive decay spectrum measured by CLEO. We also give exact large Nc relations among isospin amplitudes for B -> D(*)X and B -> D(*) D-bar(*)X, which can be used to test factorization through exclusive or inclusive measurements. Predictions for the modes B-> D(*) pi pi, B-> D(*)K K-bar and B-> D(*) D-bar(*) K are discussed using available data.Comment: 15 pages, 3 included .eps figures, minor change

Positioning of self-assembled Ge islands on stripe-patterned Si (001) substrates

Self-assembled Ge islands were grown on stripe-patterned Si (001) substrates by solid source molecular beam epitaxy. The surface morphology obtained by atomic force microscopy (AFM) and cross-sectional transmission electron microscopy images (TEM) shows that the Ge islands are preferentially grown at the sidewalls of pure Si stripes along [-110] direction at 650o C or along the trenches, whereas most of the Ge islands are formed on the top terrace when the patterned stripes are covered by a strained GeSi buffer layer. Reducing the growth temperature to 600oC results in a nucleation of Ge islands both on the top terrace and at the sidewall of pure Si stripes. A qualitative analysis, based on the growth kinetics, demonstrates that the step structure of the stripes, the external strain field and the local critical wetting layer thickness for the islands formation contribute to the preferential positioning of Ge islands on the stripes.Comment: 10 pages, 7 figures, 1 table, the original paper is in print in J. Appl. Phy

Initial stage of the 2D-3D transition of a strained SiGe layer on a pit-patterned Si(001) template

We investigate the initial stage of the 2D-3D transition of strained Ge layers deposited on pit-patterned Si(001) templates. Within the pits, which assume the shape of inverted, truncated pyramids after optimized growth of a Si buffer layer, the Ge wetting layer develops a complex morphology consisting exclusively of {105} and (001) facets. These results are attributed to a strain-driven step-meandering instability on the facetted side-walls of the pits, and a step-bunching instability at the sharp concave intersections of these facets. Although both instabilities are strain-driven, their coexistence becomes mainly possible by the geometrical restrictions in the pits. It is shown that the morphological transformation of the pit surface into low-energy facets has strong influence on the preferential nucleation of Ge islands at the flat bottom of the pits.Comment: 19 pages, 7 figure