18,671 research outputs found
Singular vectors of the algebra
The null vectors of an arbitrary highest weight representation of the
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 is not diagonalisable
among the singular vectors.Comment: 10 pages, LaTeX with 3 figures in LaTe
Null vectors of the 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 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
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