21,182 research outputs found
Topological Lensing in Spherical Spaces
This article gives the construction and complete classification of all
three-dimensional spherical manifolds, and orders them by decreasing volume, in
the context of multiconnected universe models with positive spatial curvature.
It discusses which spherical topologies are likely to be detectable by
crystallographic methods using three-dimensional catalogs of cosmic objects.
The expected form of the pair separation histogram is predicted (including the
location and height of the spikes) and is compared to computer simulations,
showing that this method is stable with respect to observational uncertainties
and is well suited for detecting spherical topologies.Comment: 32 pages, 26 figure
Hypergroups and Hypergroup Algebras
The survey contains a brief description of the ideas, constructions, results,
and prospects of the theory of hypergroups and generalized translation
operators. Representations of hypergroups are considered, being treated as
continuous representations of topological hypergroup algebras.Comment: 52 page
Multi- hexagonal spin density waves and dynamically generated spin-orbit coupling: time-reversal invariant analog of the chiral spin density wave
We study hexagonal spin-channel ("triplet") density waves with commensurate
-point propagation vectors. We first show that the three components of
the singlet charge density and charge-current density waves can be mapped to
multi-component nonzero angular momentum order in three dimensions ()
with cubic crystal symmetry. This one-to-one correspondence is exploited to
define a symmetry classification for triplet -point density waves using the
standard classification of spin-orbit coupled electronic liquid crystal phases
of a cubic crystal. Through this classification we naturally identify a set of
non-coplanar spin density and spin-current density waves: the chiral spin
density wave and its time-reversal invariant analog. These can be thought of as
and spin-orbit coupled isotropic -phase orders. In
contrast, uniaxial spin density waves are shown to correspond to
-phases. The non-coplanar triple- spin-current density wave realizes
a novel semimetal state with three flavors of four-component spin-momentum
locked Dirac cones, protected by a crystal symmetry akin to non-symmorphic
symmetry, and sits at the boundary between a trivial and topological insulator.
In addition, we point out that a special class of classical spin states,
defined as classical spin states respecting all lattice symmetries up to global
spin rotation, are naturally obtained from the symmetry classification of
electronic triplet density waves. These symmetric classical spin states are the
classical long-range ordered limits of chiral spin liquids.Comment: 14 + 4 pages, 5 + 0 figures; published versio
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