1,692 research outputs found
Dispersive estimates for Schrodinger operators in dimensions one and three
We prove L^1 --> L^\infty estimates for linear Schroedinger equations in
dimensions one and three. The potentials are only required to satisfy some mild
decay assumptions. No regularity on the potentials is assumed.Comment: 20 pages. Corrected typos and improved explanatory remarks at the en
Can we distinguish between black holes and wormholes by their Einstein-ring systems?
For the last decade, the gravitational lensing in the strong gravitational
field has been studied eagerly. It is well known that, for the lensing by a
black hole, infinite number of Einstein rings are formed by the light rays
which wind around the black hole nearly on the photon sphere, which are called
relativistic Einstein rings. This is also the case for the lensing by a
wormhole. In this paper, we study the Einstein ring and relativistic Einstein
rings for the Schwarzschild black hole and the Ellis wormhole, the latter of
which is an example of traversable wormholes of the Morris-Thorne class. Given
the configuration of the gravitational lensing and the radii of the Einstein
ring and relativistic Einstein rings, we can distinguish between a black hole
and a wormhole in principle. We conclude that we can detect the relativistic
Einstein rings by wormholes which have the radii of the throat pc
at a galactic center with the distance 10Mpc and which have AU in
our galaxy using by the most powerful modern instruments which have the
resolution of arcsecond such as a 10-meter optical-infrared telescope.
The black holes which make the Einstein rings of the same size as the ones by
the wormholes are galactic supermassive black holes and the relativistic
Einstein rings by the black holes are too small to measure at this moment. We
may test some hypotheses of astrophysical wormholes by using the Einstein ring
and relativistic Einstein rings in the future.Comment: 13 pages, 2 figures, minor changes from v
On the chiral anomaly in non-Riemannian spacetimes
The translational Chern-Simons type three-form coframe torsion on a
Riemann-Cartan spacetime is related (by differentiation) to the Nieh-Yan
four-form. Following Chandia and Zanelli, two spaces with non-trivial
translational Chern-Simons forms are discussed. We then demonstrate, firstly
within the classical Einstein-Cartan-Dirac theory and secondly in the quantum
heat kernel approach to the Dirac operator, how the Nieh-Yan form surfaces in
both contexts, in contrast to what has been assumed previously.Comment: 18 pages, RevTe
WKB analysis for nonlinear Schr\"{o}dinger equations with potential
We justify the WKB analysis for the semiclassical nonlinear Schr\"{o}dinger
equation with a subquadratic potential. This concerns subcritical, critical,
and supercritical cases as far as the geometrical optics method is concerned.
In the supercritical case, this extends a previous result by E. Grenier; we
also have to restrict to nonlinearities which are defocusing and cubic at the
origin, but besides subquadratic potentials, we consider initial phases which
may be unbounded. For this, we construct solutions for some compressible Euler
equations with unbounded source term and unbounded initial velocity.Comment: 25 pages, 11pt, a4. Appendix withdrawn, due to some inconsistencie
Reply to the comment by D. Kreimer and E. Mielke
We respond to the comment by Kreimer et. al. about the torsional contribution
to the chiral anomaly in curved spacetimes. We discuss their claims and refute
its main conclusion.Comment: 9 pages, revte
Interactive single cell RNA-Seq analysis with Single Cell Toolkit (SCTK)
I will present the Single Cell Toolkit (SCTK), an R package and interactive single cell RNA-sequencing (scRNA-Seq) analysis package that provides the first complete workflow for scRNA-Seq data analysis and visualization using a set of R functions and an interactive web interface. Users can perform analysis with modules for filtering raw results, clustering, batch correction, differential expression, pathway enrichment, and scRNA-Seq study design. The toolkit supports command line or pipeline data processing, and results can be loaded into the GUI for additional exploration and downstream analysis. We demonstrate the effectiveness of the SCTK on multiple scRNA-seq examples, including data from mucosal-associated invariant T cells, induced pluripotent stem cells, and breast cancer tumor cells. While other scRNA-Seq analysis tools exist, the SCTK is the first fully interactive analysis toolkit for scRNA-Seq data available within the R language.NIH U01CA22041
Topological Invariants, Instantons and Chiral Anomaly on Spaces with Torsion
In a spacetime with nonvanishing torsion there can occur topologically stable
configurations associated with the frame bundle which are independent of the
curvature. The relevant topological invariants are integrals of local scalar
densities first discussed by Nieh and Yan (N-Y). In four dimensions, the N-Y
form is the only closed
4-form invariant under local Lorentz rotations associated with the torsion of
the manifold. The integral of over a compact D-dimensional (Euclidean)
manifold is shown to be a topological invariant related to the Pontryagin
classes of SO(D+1) and SO(D). An explicit example of a topologically nontrivial
configuration carrying nonvanishing instanton number proportional to
is costructed. The chiral anomaly in a four-dimensional spacetime with torsion
is also shown to contain a contribution proportional to , besides the usual
Pontryagin density related to the spacetime curvature. The violation of chiral
symmetry can thus depend on the instanton number of the tangent frame bundle of
the manifold. Similar invariants can be constructed in D>4 dimensions and the
existence of the corresponding nontrivial excitations is also discussed.Comment: 6 pages, RevTeX, no figures, two column
Generation of coherent terahertz pulses in Ruby at room temperature
We have shown that a coherently driven solid state medium can potentially
produce strong controllable short pulses of THz radiation. The high efficiency
of the technique is based on excitation of maximal THz coherence by applying
resonant optical pulses to the medium. The excited coherence in the medium is
connected to macroscopic polarization coupled to THz radiation. We have
performed detailed simulations by solving the coupled density matrix and
Maxwell equations. By using a simple -type energy scheme for ruby, we have
demonstrated that the energy of generated THz pulses ranges from hundreds of
pico-Joules to nano-Joules at room temperature and micro-Joules at liquid
helium temperature, with pulse durations from picoseconds to tens of
nanoseconds. We have also suggested a coherent ruby source that lases on two
optical wavelengths and simultaneously generates THz radiation. We discussed
also possibilities of extension of the technique to different solid-state
materials
Pure Point Spectrum of the Floquet Hamiltonian for the Quantum Harmonic Oscillator Under Time Quasi- Periodic Perturbations
We prove that the quantum harmonic oscillator is stable under spatially
localized, time quasi-periodic perturbations on a set of Diophantine
frequencies of positive measure. This proves a conjecture raised by
Enss-Veselic in their 1983 paper \cite{EV} in the general quasi-periodic
setting. The motivation of the present paper also comes from construction of
quasi-periodic solutions for the corresponding nonlinear equation
Black hole solutions in Euler-Heisenberg theory
We construct static and spherically symmetric black hole solutions in the
Einstein-Euler-Heisenberg (EEH) system which is considered as an effective
action of a superstring theory. We considered electrically charged,
magnetically charged and dyon solutions. We can solve analytically for the
magnetically charged case. We find that they have some remarkable properties
about causality and black hole thermodynamics depending on the coupling
constant of the EH theory and , though they have central singularity as
in the Schwarzschild black hole.Comment: 8 pages, 13 figures, figures corrected and some comments adde
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