149,706 research outputs found
Hopf characterization of two-dimensional Floquet topological insulators
We present a topological characterization of time-periodically driven
two-band models in 2+1 dimensions as Hopf insulators. The intrinsic periodicity
of the Floquet system with respect to both time and the underlying
two-dimensional momentum space constitutes a map from a three dimensional torus
to the Bloch sphere. As a result, we find that the driven system can be
understood by appealing to a Hopf map that is directly constructed from the
micromotion of the drive. Previously found winding numbers are shown to
correspond to Hopf invariants, which are associated with linking numbers
describing the topology of knots in three dimensions. Moreover, after being
cast as a Hopf insulator, not only the Chern numbers, but also the winding
numbers of the Floquet topological insulator become accessible in experiments
as linking numbers. We exploit this description to propose a feasible scheme
for measuring the complete set of their Floquet topological invariants in
optical lattices.Comment: 6 pages, 3 figures + 2 pages, 1 figure supplementar
Shaped Pupil Lyot Coronagraphs: High-Contrast Solutions for Restricted Focal Planes
Coronagraphs of the apodized pupil and shaped pupil varieties use the
Fraunhofer diffraction properties of amplitude masks to create regions of high
contrast in the vicinity of a target star. Here we present a hybrid coronagraph
architecture in which a binary, hard-edged shaped pupil mask replaces the gray,
smooth apodizer of the apodized pupil Lyot coronagraph (APLC). For any contrast
and bandwidth goal in this configuration, as long as the prescribed region of
contrast is restricted to a finite area in the image, a shaped pupil is the
apodizer with the highest transmission. We relate the starlight cancellation
mechanism to that of the conventional APLC. We introduce a new class of
solutions in which the amplitude profile of the Lyot stop, instead of being
fixed as a padded replica of the telescope aperture, is jointly optimized with
the apodizer. Finally, we describe shaped pupil Lyot coronagraph (SPLC) designs
for the baseline architecture of the Wide-Field Infrared Survey
Telescope-Astrophysics Focused Telescope Assets (WFIRST-AFTA) coronagraph.
These SPLCs help to enable two scientific objectives of the WFIRST-AFTA
mission: (1) broadband spectroscopy to characterize exoplanet atmospheres in
reflected starlight and (2) debris disk imaging.Comment: 41 pages, 15 figures; published in the JATIS special section on
WFIRST-AFTA coronagraph
Exploring the Interplay between Virology and Molecular Crystallography
Polyhedra with icosahedral symmetry and vertices labelled by rational indices of points of a six-dimensional lattice left invariant by the icosahedral group allow a morphological characterization of icosahedral viruses which includes the Caspar–Klug classification as a special case. Scaling transformations relating the indexed polyhedron enclosing the surface with the one delimiting the central cavity lead to models of viral capsids observed in nature. Similar scaling relations can be obtained from projected images in three dimensions of higher-dimensional crystallographic point groups having the icosahedral group as a subgroup. This crystallographic approach can be extended to axial-symmetric clusters of coat proteins around icosahedral axes of the capsid. One then gets enclosing forms with vertices at points of lattices left invariant by the corresponding point group and having additional crystallographic properties also observed in natural crystals, but not explained by the known crystallographic laws
Some intriguing properties of Tukey's half-space depth
For multivariate data, Tukey's half-space depth is one of the most popular
depth functions available in the literature. It is conceptually simple and
satisfies several desirable properties of depth functions. The Tukey median,
the multivariate median associated with the half-space depth, is also a
well-known measure of center for multivariate data with several interesting
properties. In this article, we derive and investigate some interesting
properties of half-space depth and its associated multivariate median. These
properties, some of which are counterintuitive, have important statistical
consequences in multivariate analysis. We also investigate a natural extension
of Tukey's half-space depth and the related median for probability
distributions on any Banach space (which may be finite- or
infinite-dimensional) and prove some results that demonstrate anomalous
behavior of half-space depth in infinite-dimensional spaces.Comment: Published in at http://dx.doi.org/10.3150/10-BEJ322 the Bernoulli
(http://isi.cbs.nl/bernoulli/) by the International Statistical
Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm
A construction of a skewaffine structure in Laguerre geometry
J. Andre constructed a skewaffine structure as a group space of a normally
transitive group. In the paper this construction was used to describe such an
external structure associated with a point of Laguerre plane. Necessary
conditions for ensure that the external structure is a skewaffine plane are
given.Comment: 10
Data depth and floating body
Little known relations of the renown concept of the halfspace depth for
multivariate data with notions from convex and affine geometry are discussed.
Halfspace depth may be regarded as a measure of symmetry for random vectors. As
such, the depth stands as a generalization of a measure of symmetry for convex
sets, well studied in geometry. Under a mild assumption, the upper level sets
of the halfspace depth coincide with the convex floating bodies used in the
definition of the affine surface area for convex bodies in Euclidean spaces.
These connections enable us to partially resolve some persistent open problems
regarding theoretical properties of the depth
Asymptotic Symmetries, Holography and Topological Hair
Asymptotic symmetries of AdS quantum gravity and gauge theory are derived
by coupling the dual CFT to Chern-Simons gauge theory and 3D gravity in a
"probe" large-level limit. The infinite-dimensional symmetries are shown to
arise when one is restricted to boundary subspaces with effectively
two-dimensional geometry. A canonical example of such a restriction occurs
within the 4D subregion described by a Wheeler-DeWitt wavefunctional of AdS
quantum gravity. An AdS analog of Minkowski "super-rotation" asymptotic
symmetry is probed by 3D Einstein gravity, yielding CFT structure, via
AdS foliation of AdS and the AdS/CFT correspondence. The
maximal asymptotic symmetry is however probed by 3D conformal gravity. Both 3D
gravities have Chern-Simons formulation, manifesting their topological
character. Chern-Simons structure is also shown to be emergent in the Poincare
patch of AdS, as soft/boundary limits of 4D gauge theory, rather than "put
in by hand", with a finite effective Chern-Simons level. Several of the
considerations of asymptotic symmetry structure are found to be simpler for
AdS than for Mink, such as non-zero 4D particle masses, 4D
non-perturbative "hard" effects, and consistency with unitarity. The last of
these, in particular, is greatly simplified, because in some set-ups the time
dimension is explicitly shared by each level of description: Lorentzian
AdS, CFT and CFT. The CFT structure clarifies the sense in
which the infinite asymptotic charges constitute a useful form of "hair" for
black holes and other complex 4D states. An AdS (holographic) "shadow"
analog of Minkowski "memory" effects is derived. Lessons from AdS provide
hints for better understanding Minkowski asymptotic symmetries, the 3D
structure of its soft limits, and Minkowski holography.Comment: typos corrected, references added, discussions of boundary conditions
corrected and clarifie
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