242,486 research outputs found
Cancellations Amongst Kloosterman Sums
We obtain several estimates for bilinear form with Kloosterman sums. Such
results can be interpreted as a measure of cancellations amongst with
parameters from short intervals. In particular, for certain ranges of
parameters we improve some recent results of Blomer, Fouvry, Kowalski, Michel,
and Mili\'cevi\'c (2014) and Fouvry, Kowalski and Michel (2014).Comment: 10 page
Stability of exact force-free electrodynamic solutions and scattering from spacetime curvature
Recently, a family of exact force-free electrodynamic (FFE) solutions was
given by Brennan, Gralla and Jacobson, which generalizes earlier solutions by
Michel, Menon and Dermer, and other authors. These solutions have been proposed
as useful models for describing the outer magnetosphere of conducting stars. As
with any exact analytical solution that aspires to describe actual physical
systems, it is vitally important that the solution possess the necessary
stability. In this paper, we show via fully nonlinear numerical simulations
that the aforementioned FFE solutions, despite being highly special in their
properties, are nonetheless stable under small perturbations. Through this
study, we also introduce a three-dimensional pseudospectral relativistic FFE
code that achieves exponential convergence for smooth test cases, as well as
two additional well-posed FFE evolution systems in the appendix that have
desirable mathematical properties. Furthermore, we provide an explicit analysis
that demonstrates how propagation along degenerate principal null directions of
the spacetime curvature tensor simplifies scattering, thereby providing an
intuitive understanding of why these exact solutions are tractable, i.e. why
they are not backscattered by spacetime curvature.Comment: 33 pages, 21 figures; V2 updated to match published versio
Switching ferromagnetic spins by an ultrafast laser pulse: Emergence of giant optical spin-orbit torque
Faster magnetic recording technology is indispensable to massive data storage
and big data sciences. {All-optical spin switching offers a possible solution},
but at present it is limited to a handful of expensive and complex rare-earth
ferrimagnets. The spin switching in more abundant ferromagnets may
significantly expand the scope of all-optical spin switching. Here by studying
40,000 ferromagnetic spins, we show that it is the optical spin-orbit torque
that determines the course of spin switching in both ferromagnets and
ferrimagnets. Spin switching occurs only if the effective spin angular momentum
of each constituent in an alloy exceeds a critical value. Because of the strong
exchange coupling, the spin switches much faster in ferromagnets than
weakly-coupled ferrimagnets. This establishes a paradigm for all-optical spin
switching. The resultant magnetic field (65 T) is so big that it will
significantly reduce high current in spintronics, thus representing the
beginning of photospintronics.Comment: 12 page2, 6 figures. Accepted to Europhysics Letters (2016). Extended
version with the supplementary information. Contribution from Indiana State
University,Europhysics Letters (2016
A fundamental limit to the efficiency of spin-exchange optical pumping of 3He nuclei
We establish the existence of a fundamental limit to the efficiency of
spin-exchange optical pumping of 3He nuclei by collisions with spin-polarized
alkali-metal atoms. Using accurate ab initio calculations of molecular
interactions and scattering properties, we show that the maximum 3He spin
polarization that can be achieved in spin-exchange collisions with potassium
(39K) and silver (107Ag) atoms is limited by the anisotropic hyperfine
interaction. We find that spin exchange in Ag-He collisions occurs much faster
than in K-He collisions, suggesting the possibility of using Ag in
spin-exchange optical pumping experiments to increase the production rate of
hyperpolarized 3He. Our analysis indicates that measurements of trap loss rates
of 2S atoms in the presence of cold 3He gas may be used to probe anisotropic
spin-exchange interactions in atom-He collisions.Comment: 5 pages, 4 figure
On the Magic Matrix by Makhlin and the B-C-H Formula in SO(4)
A closed expression to the Baker-Campbell-Hausdorff (B-C-H) formula in SO(4)
is given by making use of the magic matrix by Makhlin. As far as we know this
is the {\bf first nontrivial example} on (semi-) simple Lie groups summing up
all terms in the B-C-H expansion.Comment: Latex ; 11 pages ; 1 figure ; minor changes. To appear in
International Journal of Geometric Methods in Modern Physics (vol.4, no.5 or
6), 200
- …