468 research outputs found

### Analysis on singular spaces : Lie manifolds and operator algebras

We discuss and develop some connections between analysis on singular spaces
and operator algebras, as presented in my sequence of four lectures at the
conference "Noncommutative geometry and applications," Frascati, Italy, June
16-21, 2014. Therefore this paper is mostly a survey paper, but the
presentation is new, and there are included some new results as well. In
particular, Sections 3 and 4 provide a complete short introduction to analysis
on noncompact manifolds that is geared towards a class of manifolds--called
"Lie manifolds"--that often appears in practice. Our interest in Lie manifolds
is due to the fact that they provide the link between analysis on singular
spaces and operator algebras. The groupoids integrating Lie manifolds play an
important background role in establishing this link because they provide
operator algebras whose structure is often well understood. The initial
motivation for the work surveyed here--work that spans over close to two
decades--was to develop the index theory of stratified singular spaces.
Meanwhile, several other applications have emerged as well, including
applications to Partial Differential Equations and Numerical Methods. These
will be mentioned only briefly, however, due to the lack of space. Instead, we
shall concentrate on the applications to Index theory.Comment: 43 pages, based on my four lectures at the conference "Noncommutative
geometry and applications," Frascati, Italy, June 16-21, 201

### Exchange stiffness in ultrathin perpendicularly-magnetized CoFeB layers determined using spin wave spectroscopy

We measure the frequencies of spin waves in nm-thick perpendicularly
magnetized FeCoB systems, and model the frequencies to deduce the exchange
stiffness of this material in the ultrathin limit. For this, we embody the
layers in magnetic tunnel junctions patterned into circular nanopillars of
diameters ranging from 100 to 300 nm and we use magneto-resistance to determine
which rf-current frequencies are efficient in populating the spin wave modes.
Micromagnetic calculations indicate that the ultrathin nature of the layer and
the large wave vectors used ensure that the spin wave frequencies are
predominantly determined by the exchange stiffness, such that the number of
modes in a given frequency window can be used to estimate the exchange. For 1
nm layers the experimental data are consistent with an exchange stiffness A= 20
pJ/m, which is slightly lower that its bulk counterpart. The thickness
dependence of the exchange stiffness has strong implications for the numerous
situations that involve ultrathin films hosting strong magnetization gradients,
and the micromagnetic description thereof.Comment: 5 pages, 4 figures, submitted to PR

### Fredholm conditions for invariant operators: finite abelian groups and boundary value problems

We answer the question of when an invariant pseudodifferential operator is Fredholm on a fixed, given isotypical component. More precisely, let $\Gamma$ be a compact group acting on a smooth, compact, manifold $M$ without boundary and let $P \in \psi^m(M; E_0, E_1)$ be a $\Gamma$-invariant, classical, pseudodifferential operator acting between sections of two $\Gamma$-equivariant vector bundles $E_0$ and $E_1$. Let $\alpha$ be an irreducible representation of the group $\Gamma$. Then $P$ induces by restriction a map $\pi_\alpha(P) : H^s(M; E_0)_\alpha \to H^{s-m}(M; E_1)_\alpha$ between the $\alpha$-isotypical components of the corresponding Sobolev spaces of sections. We study in this paper conditions on the map $\pi_\alpha(P)$ to be Fredholm. It turns out that the discrete and non-discrete cases are quite different. Additionally, the discrete abelian case, which provides some of the most interesting applications, presents some special features and is much easier than the general case. We thus concentrate in this paper on the case when $\Gamma$ is finite abelian. We prove then that the restriction $\pi_\alpha(P)$ is Fredholm if, and only if, $P$ is "$\alpha$-elliptic", a condition defined in terms of the principal symbol of $P$. If $P$ is elliptic, then $P$ is also $\alpha$-elliptic, but the converse is not true in general. However, if $\Gamma$ acts freely on a dense open subset of $M$, then $P$ is $\alpha$-elliptic for the given fixed $\alpha$ if, and only if, it is elliptic. The proofs are based on the study of the structure of the algebra $\psi^{m}(M; E)^\Gamma$ of classical, $\Gamma$-invariant pseudodifferential operators acting on sections of the vector bundle $E \to M$ and of the structure of its restrictions to the isotypical components of $\Gamma$. These structures are described in terms of the isotropy groups of the action of the group $\Gamma$ on $E \to M$

### 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 $M$. A main ingredient is a non-commutative algebra
that plays in our setting the role of $C_0(T^*M)$. We prove a Thom isomorphism
between non-commutative algebras which gives a new example of wrong way
functoriality in $K$-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

### Novel types of anti-ecloud surfaces

In high power RF devices for space, secondary electron emission appears as
the main parameter governing the multipactor effect and as well as the e-cloud
in large accelerators. Critical experimental activities included development of
coatings with low secondary electron emission yield (SEY) for steel (large
accelerators) and aluminium (space applications). Coatings with surface
roughness of high aspect ratio producing the so-call secondary emission
suppression effect appear as the selected strategy. In this work a detailed
study of the SEY of these technological coatings and also the experimental
deposition methods (PVD and electrochemical) are presented. The coating-design
approach selected for new low SEY coatings include rough metals (Ag, Au, Al),
rough alloys (NEG), particulated and magnetized surfaces, and also graphene
like coatings. It was found that surface roughness also mitigate the SEY
deterioration due to aging processes.Comment: 4 pages, contribution to the Joint INFN-CERN-EuCARD-AccNet Workshop
on Electron-Cloud Effects: ECLOUD'12; 5-9 Jun 2012, La Biodola, Isola d'Elba,
Italy; CERN Yellow Report CERN-2013-002, pp.153-15

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