320 research outputs found
Groupoids and an index theorem for conical pseudo-manifolds
We define an analytical index map and a topological index map for conical
pseudomanifolds. These constructions generalize the analogous constructions
used by Atiyah and Singer in the proof of their topological index theorem for a
smooth, compact manifold . A main ingredient is a non-commutative algebra
that plays in our setting the role of . We prove a Thom isomorphism
between non-commutative algebras which gives a new example of wrong way
functoriality in -theory. We then give a new proof of the Atiyah-Singer
index theorem using deformation groupoids and show how it generalizes to
conical pseudomanifolds. We thus prove a topological index theorem for conical
pseudomanifolds
Spin injection in Silicon at zero magnetic field
In this letter, we show efficient electrical spin injection into a SiGe based
\textit{p-i-n} light emitting diode from the remanent state of a
perpendicularly magnetized ferromagnetic contact. Electron spin injection is
carried out through an alumina tunnel barrier from a Co/Pt thin film exhibiting
a strong out-of-plane anisotropy. The electrons spin polarization is then
analysed through the circular polarization of emitted light. All the light
polarization measurements are performed without an external applied magnetic
field \textit{i.e.} in remanent magnetic states. The light polarization as a
function of the magnetic field closely traces the out-of-plane magnetization of
the Co/Pt injector. We could achieve a circular polarization degree of the
emitted light of 3 % at 5 K. Moreover this light polarization remains almost
constant at least up to 200 K.Comment: accepted in AP
Muon capture on light nuclei
This work investigates the muon capture reactions 2H(\mu^-,\nu_\mu)nn and
3He(\mu^-,\nu_\mu)3H and the contribution to their total capture rates arising
from the axial two-body currents obtained imposing the
partially-conserved-axial-current (PCAC) hypothesis. The initial and final A=2
and 3 nuclear wave functions are obtained from the Argonne v_{18} two-nucleon
potential, in combination with the Urbana IX three-nucleon potential in the
case of A=3. The weak current consists of vector and axial components derived
in chiral effective field theory. The low-energy constant entering the vector
(axial) component is determined by reproducting the isovector combination of
the trinucleon magnetic moment (Gamow-Teller matrix element of tritium
beta-decay). The total capture rates are 393.1(8) s^{-1} for A=2 and 1488(9)
s^{-1} for A=3, where the uncertainties arise from the adopted fitting
procedure.Comment: 6 pages, submitted to Few-Body Sys
The topological dimension of type I C*-algebras
While there is only one natural dimension concept for separable, metric
spaces, the theory of dimension in noncommutative topology ramifies into
different important concepts. To accommodate this, we introduce the abstract
notion of a noncommutative dimension theory by proposing a natural set of
axioms. These axioms are inspired by properties of commutative dimension
theory, and they are for instance satisfied by the real and stable rank, the
decomposition rank and the nuclear dimension.
We add another theory to this list by showing that the topological dimension,
as introduced by Brown and Pedersen, is a noncommutative dimension theory of
type I C*-algebras. We also give estimates of the real and stable rank of a
type I C*-algebra in terms of its topological dimension.Comment: 20 pages; minor correction
The Dirac operator on generalized Taub-NUT spaces
We find sufficient conditions for the absence of harmonic spinors on
spin manifolds constructed as cone bundles over a compact K\"ahler base. These
conditions are fulfilled for certain perturbations of the Euclidean metric, and
also for the generalized Taub-NUT metrics of Iwai-Katayama, thus proving a
conjecture of Vi\csinescu and the second author.Comment: Final version, 16 page
Regularity for eigenfunctions of Schr\"odinger operators
We prove a regularity result in weighted Sobolev spaces (or
Babuska--Kondratiev spaces) for the eigenfunctions of a Schr\"odinger operator.
More precisely, let K_{a}^{m}(\mathbb{R}^{3N}) be the weighted Sobolev space
obtained by blowing up the set of singular points of the Coulomb type potential
V(x) = \sum_{1 \le j \le N} \frac{b_j}{|x_j|} + \sum_{1 \le i < j \le N}
\frac{c_{ij}}{|x_i-x_j|}, x in \mathbb{R}^{3N}, b_j, c_{ij} in \mathbb{R}. If u
in L^2(\mathbb{R}^{3N}) satisfies (-\Delta + V) u = \lambda u in distribution
sense, then u belongs to K_{a}^{m} for all m \in \mathbb{Z}_+ and all a \le 0.
Our result extends to the case when b_j and c_{ij} are suitable bounded
functions on the blown-up space. In the single-electron, multi-nuclei case, we
obtain the same result for all a<3/2.Comment: to appear in Lett. Math. Phy
Regularity of the eta function on manifolds with cusps
On a spin manifold with conformal cusps, we prove under an invertibility
condition at infinity that the eta function of the twisted Dirac operator has
at most simple poles and is regular at the origin. For hyperbolic manifolds of
finite volume, the eta function of the Dirac operator twisted by any
homogeneous vector bundle is shown to be entire.Comment: 22 pages, 2 figure
Slow Magnetic Relaxation of Dy Adatoms with In-Plane Magnetic Anisotropy on a Two-Dimensional Electron Gas
We report on the magnetic properties of Dy atoms adsorbed on the (001) surface of SrTiO3. X-ray magnetic circular dichroism reveals slow relaxation of the Dy magnetization on a time scale of about 800 s at 2.5 K, unusually associated with an easy-plane magnetic anisotropy. We attribute these properties to Dy atoms occupying hollow adsorption sites on the TiO2-terminated surface. Conversely, Ho atoms adsorbed on the same surface show paramagnetic behavior down to 2.5 K. With the help of atomic multiplet simulations and first-principles calculations, we establish that Dy populates also the top-O and bridge sites on the coexisting SrO-terminated surface. A simple magnetization relaxation model predicts these two sites to have an even longer magnetization lifetime than the hollow site. Moreover, the adsorption of Dy on the insulating SrTiO3 crystal leads, regardless of the surface termination, to the formation of a spin-polarized two-dimensional electron gas of Ti 3dxy character, together with an antiferromagnetic Dy-Ti coupling. Our findings support the feasibility of tuning the magnetic properties of the rare-earth atoms by acting on the substrate electronic gas with electric fields.We acknowldege funding from the National Research Council (CNR) within the CNR/CAS Cooperative Programme project "Advanced characterization methods for the study of rare-earth single-ion magnets on oxide substrates", from the Czech Academy of Sciences (Mobility Plus Project No. CNR-19-03), and from the Swiss National Science Foundation (200020_176932 and 200021_175941). ICN2 was funded by the CERCA Programme/Generalitat de Catalunya and supported by the Spanish Ministry of Economy and Competitiveness, MINECO (grant nos. SEV-2017-0706 and PID2019-107338RB-C65/AEI/10.13039/501100011033). IMDEA Nanociencia acknowledges support from the Severo Ochoa Programme for Centres of Excellence in R&D (MINECO, grant SEV-2016-0686).Peer reviewe
Equivalence of Conventionally-Derived and Parthenote-Derived Human Embryonic Stem Cells
As human embryonic stem cell (hESC) lines can be derived via multiple means, it is important to determine particular characteristics of individual lines that may dictate the applications to which they are best suited. The objective of this work was to determine points of equivalence and differences between conventionally-derived hESC and parthenote-derived hESC lines (phESC) in the undifferentiated state and during neural differentiation.hESC and phESC were exposed to the same expansion conditions and subsequent neural and retinal pigmented epithelium (RPE) differentiation protocols. Growth rates and gross morphology were recorded during expansion. RTPCR for developmentally relevant genes and global DNA methylation profiling were used to compare gene expression and epigenetic characteristics. Parthenote lines proliferated more slowly than conventional hESC lines and yielded lower quantities of less mature differentiated cells in a neural progenitor cell (NPC) differentiation protocol. However, the cell lines performed similarly in a RPE differentiation protocol. The DNA methylation analysis showed similar general profiles, but the two cell types differed in methylation of imprinted genes. There were no major differences in gene expression between the lines before differentiation, but when differentiated into NPCs, the two cell types differed in expression of extracellular matrix (ECM) genes.These data show that hESC and phESC are similar in the undifferentiated state, and both cell types are capable of differentiation along neural lineages. The differences between the cell types, in proliferation and extent of differentiation, may be linked, in part, to the observed differences in ECM synthesis and methylation of imprinted genes
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