12,770 research outputs found
Overlap properties of geometric expanders
The {\em overlap number} of a finite -uniform hypergraph is
defined as the largest constant such that no matter how we map
the vertices of into , there is a point covered by at least a
-fraction of the simplices induced by the images of its hyperedges.
In~\cite{Gro2}, motivated by the search for an analogue of the notion of graph
expansion for higher dimensional simplicial complexes, it was asked whether or
not there exists a sequence of arbitrarily large
-uniform hypergraphs with bounded degree, for which . Using both random methods and explicit constructions, we answer this
question positively by constructing infinite families of -uniform
hypergraphs with bounded degree such that their overlap numbers are bounded
from below by a positive constant . We also show that, for every ,
the best value of the constant that can be achieved by such a
construction is asymptotically equal to the limit of the overlap numbers of the
complete -uniform hypergraphs with vertices, as
. For the proof of the latter statement, we establish the
following geometric partitioning result of independent interest. For any
and any , there exists satisfying the
following condition. For any , for any point and
for any finite Borel measure on with respect to which
every hyperplane has measure , there is a partition into measurable parts of equal measure such that all but
at most an -fraction of the -tuples
have the property that either all simplices with
one vertex in each contain or none of these simplices contain
Optical patterning of trapped charge in nitrogen-doped diamond
The nitrogen-vacancy (NV) centre in diamond is emerging as a promising
platform for solid-state quantum information processing and nanoscale
metrology. Of interest in these applications is the manipulation of the NV
charge, which can be attained by optical excitation. Here we use two-color
optical microscopy to investigate the dynamics of NV photo-ionization, charge
diffusion, and trapping in type-1b diamond. We combine fixed-point laser
excitation and scanning fluorescence imaging to locally alter the concentration
of negatively charged NVs, and to subsequently probe the corresponding
redistribution of charge. We uncover the formation of spatial patterns of
trapped charge, which we qualitatively reproduce via a model of the interplay
between photo-excited carriers and atomic defects. Further, by using the NV as
a probe, we map the relative fraction of positively charged nitrogen upon
localized optical excitation. These observations may prove important to
transporting quantum information between NVs or to developing
three-dimensional, charge-based memories
SM(2,4k) fermionic characters and restricted jagged partitions
A derivation of the basis of states for the superconformal minimal
models is presented. It relies on a general hypothesis concerning the role of
the null field of dimension . The basis is expressed solely in terms of
modes and it takes the form of simple exclusion conditions (being thus a
quasi-particle-type basis). Its elements are in correspondence with
-restricted jagged partitions. The generating functions of the latter
provide novel fermionic forms for the characters of the irreducible
representations in both Ramond and Neveu-Schwarz sectors.Comment: 12 page
Long-Baseline Interferometric Multiplicity Survey of the Sco-Cen OB Association
We present the first multiplicity-dedicated long baseline optical
interferometric survey of the Scorpius-Centaurus-Lupus-Crux association. We
used the Sydney University Stellar Interferometer to undertake a survey for new
companions to 58 Sco-Cen B- type stars and have detected 24 companions at
separations ranging from 7-130mas, 14 of which are new detections. Furthermore,
we use a Bayesian analysis and all available information in the literature to
determine the multiplicity distribution of the 58 stars in our sample, showing
that the companion frequency is F = 1.35 and the mass ratio distribution is
best described as a power law with exponent equal to -0.46, agreeing with
previous Sco-Cen high mass work and differing significantly from lower-mass
stars in Tau-Aur. Based on our analysis, we estimate that among young B-type
stars in moving groups, up to 23% are apparently single stars. This has strong
implications for the understanding of high-mass star formation, which requires
angular momentum dispersal through some mechanism such as formation of multiple
systems.Comment: 7 figures, 5 tables, accepted for publication in MNRA
Precise Experimental Investigation of Eigenmodes in a Planar Ion Crystal
The accurate characterization of eigenmodes and eigenfrequencies of
two-dimensional ion crystals provides the foundation for the use of such
structures for quantum simulation purposes. We present a combined experimental
and theoretical study of two-dimensional ion crystals. We demonstrate that
standard pseudopotential theory accurately predicts the positions of the ions
and the location of structural transitions between different crystal
configurations. However, pseudopotential theory is insufficient to determine
eigenfrequencies of the two-dimensional ion crystals accurately but shows
significant deviations from the experimental data obtained from resolved
sideband spectroscopy. Agreement at the level of 2.5 x 10^(-3) is found with
the full time-dependent Coulomb theory using the Floquet-Lyapunov approach and
the effect is understood from the dynamics of two-dimensional ion crystals in
the Paul trap. The results represent initial steps towards an exploitation of
these structures for quantum simulation schemes.Comment: 5 pages, 4 figures, supplemental material (mathematica and matlab
files) available upon reques
Potential of observations from the Tropospheric Emission Spectrometer to constrain continental sources of carbon monoxide
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