29,780 research outputs found
Reconstruction of Binary Functions and Shapes from Incomplete Frequency Information
The characterization of a binary function by partial frequency information is
considered. We show that it is possible to reconstruct binary signals from
incomplete frequency measurements via the solution of a simple linear
optimization problem. We further prove that if a binary function is spatially
structured (e.g. a general black-white image or an indicator function of a
shape), then it can be recovered from very few low frequency measurements in
general. These results would lead to efficient methods of sensing,
characterizing and recovering a binary signal or a shape as well as other
applications like deconvolution of binary functions blurred by a low-pass
filter. Numerical results are provided to demonstrate the theoretical
arguments.Comment: IEEE Transactions on Information Theory, 201
Robustness of Majorana Modes and Minigaps in a Spin-Orbit-Coupled Semiconductor-Superconductor Heterostructure
We study the robustness of Majorana zero energy modes and minigaps of
quasiparticle excitations in a vortex by numerically solving
Bogoliubov-deGennes equations in a heterostructure composed of an \textit{s}
-wave superconductor, a spin-orbit-coupled semiconductor thin film, and a
magnetic insulator. This heterostructure was proposed recently as a platform
for observing non-Abelian statistics and performing topological quantum
computation. The dependence of the Majorana zero energy states and the minigaps
on various physics parameters (Zeeman field, chemical potential, spin-orbit
coupling strength) is characterized. We find the minigaps depend strongly on
the spin-orbit coupling strength. In certain parameter region, the minigaps are
linearly proportional to the \textit{s}-wave superconducting pairing gap
, which is very different from the dependence in a
regular \textit{s-} or \textit{\p}-wave superconductor. We characterize the
zero energy chiral edge state at the boundary and calculate the STM signal in
the vortex core that shows a pronounced zero energy peak. We show that the
Majorana zero energy states are robust in the presence of various types of
impurities. We find the existence of impurity potential may increase the
minigaps and thus benefit topological quantum computation.Comment: 11 pages, 15 figure
Microlensing of Sub-parsec Massive Binary Black Holes in Lensed QSOs: Light Curves and Size-Wavelength Relation
Sub-parsec binary massive black holes (BBHs) are long anticipated to exist in
many QSOs but remain observationally elusive. In this paper, we propose a novel
method to probe sub-parsec BBHs through microlensing of lensed QSOs. If a QSO
hosts a sub-parsec BBH in its center, it is expected that the BBH is surrounded
by a circum-binary disk, each component of the BBH is surrounded by a small
accretion disk, and a gap is opened by the secondary component in between the
circum-binary disk and the two small disks. Assuming such a BBH structure, we
generate mock microlensing light curves for some QSO systems that host BBHs
with typical physical parameters. We show that microlensing light curves of a
BBH QSO system at the infrared-optical-UV bands can be significantly different
from those of corresponding QSO system with a single massive black hole (MBH),
mainly because of the existence of the gap and the rotation of the BBH (and its
associated small disks) around the center of mass. We estimate the half-light
radii of the emission region at different wavelengths from mock light curves
and find that the obtained half-light radius vs. wavelength relations of BBH
QSO systems can be much flatter than those of single MBH QSO systems at a
wavelength range determined by the BBH parameters, such as the total mass, mass
ratio, separation, accretion rates, etc. The difference is primarily due to the
existence of the gap. Such unique features on the light curves and half-light
radius-wavelength relations of BBH QSO systems can be used to select and probe
sub-parsec BBHs in a large number of lensed QSOs to be discovered by current
and future surveys, including the Panoramic Survey Telescope and Rapid Response
System (Pan-STARRS), the Large Synoptic Survey telescope (LSST) and Euclid.Comment: 18 pages, 17 figures, accepted for publication in the Astrophysical
Journa
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