36,172 research outputs found
Magnetotransport and magnetocrystalline anisotropy in Ga1-xMnxAs epilayers
We present an analysis of the magnetic anisotropy in epitaxial Ga1-xMnxAs thin films through electrical transport measurements on multiterminal microdevices. The film magnetization is manipulated in 3D space by a three-axis vector magnet. Anomalous switching patterns are observed in both longitudinal and transverse resistance data. In transverse geometry in particular we observe strong interplay between the anomalous Hall effect and the giant planar Hall effect. This allows direct electrical characterization of magnetic transitions in the 3D space. These transitions reflect a competition between cubic magnetic anisotropy and an effective out-of-plane uniaxial anisotropy, with a reversal mechanism that is distinct from the in-plane magnetization. The uniaxial anisotropy field is directly calculated with high precision and compared with theoretical predictions
Cyclic cocycles on deformation quantizations and higher index theorems
We construct a nontrivial cyclic cocycle on the Weyl algebra of a symplectic
vector space. Using this cyclic cocycle we construct an explicit, local,
quasi-isomorphism from the complex of differential forms on a symplectic
manifold to the complex of cyclic cochains of any formal deformation
quantization thereof. We give a new proof of Nest-Tsygan's algebraic higher
index theorem by computing the pairing between such cyclic cocycles and the
-theory of the formal deformation quantization. Furthermore, we extend this
approach to derive an algebraic higher index theorem on a symplectic orbifold.
As an application, we obtain the analytic higher index theorem of
Connes--Moscovici and its extension to orbifolds.Comment: 59 pages, this is a major revision, orbifold analytic higher index is
introduce
The transverse index theorem for proper cocompact actions of Lie groupoids
Given a proper, cocompact action of a Lie groupoid, we define a higher index
pairing between invariant elliptic differential operators and smooth groupoid
cohomology classes. We prove a cohomological index formula for this pairing by
applying the van Est map and algebraic index theory. Finally we discuss in
examples the meaning of the index pairing and our index formula.Comment: 29 page
The index of geometric operators on Lie groupoids
We revisit the cohomological index theorem for elliptic elements in the
universal enveloping algebra of a Lie groupoid previously proved by the
authors. We prove a Thom isomorphism for Lie algebroids which enables us to
rewrite the "topological side" of the index theorem. This results in index
formulae for Lie groupoid analogues of the familiar geometric operators on
manifolds such as the signature and Dirac operator expressed in terms of the
usual characteristic classes in Lie algebroid cohomology.Comment: 15 page
Quantization of Whitney functions
We propose to study deformation quantizations of Whitney functions. To this
end, we extend the notion of a deformation quantization to algebras of Whitney
functions over a singular set, and show the existence of a deformation
quantization of Whitney functions over a closed subset of a symplectic
manifold. Under the assumption that the underlying symplectic manifold is
analytic and the singular subset subanalytic, we determine that the Hochschild
and cyclic homology of the deformed algebra of Whitney functions over the
subanalytic subset coincide with the Whitney--de Rham cohomology. Finally, we
note how an algebraic index theorem for Whitney functions can be derived.Comment: 10 page
Magnetoelectronic Phenomena at a Ferromagnet-Semiconductor Interface
A Comment on the Letter by P. R. Hammar et al., Phys. Rev. Lett. 83, 203 (1999)
Effect of borehole stress concentration on compressional wave velocity measurements
Formation elastic properties near a borehole may be altered from their original state due to the stress concentration around the borehole. This could lead to a biased estimation of formation elastic properties measured from sonic logging data. To study the effect of stress concentration around a borehole on sonic logging, we first use an iterative approach, which combines a rock physics model and a finite-element method, to calculate the stress-dependent elastic properties of the rock around a borehole when it is subjected to an anisotropic stress loading. Then we use the anisotropic elastic model obtained from the first step and a finite-difference method to simulate the acoustic response in a borehole. Our numerical results are consistent with published laboratory measurements of the azimuthal velocity variations caused by borehole stress concentration. Both numerical and experimental results show that the variation of P-wave velocity versus azimuth has broad maxima and cusped minima, which is different from the presumed cosine behavior. This is caused by the preference of the wavefield to propagate through a higher velocity region
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