19,665 research outputs found
Transition-Metal Pentatelluride ZrTe and HfTe: a Paradigm for Large-gap Quantum Spin Hall Insulators
Quantum spin Hall (QSH) insulators, a new class of quantum matters, can
support topologically protected helical edge modes inside bulk insulating gap,
which can lead to dissipationless transport. A major obstacle to reach wide
application of QSH is the lack of suitable QSH compounds, which should be
easily fabricated and has large size of bulk gap. Here we predict that single
layer ZrTe and HfTe are the most promising candidates to reach the
large gap QSH insulators with bulk direct (indirect) band gap as large as 0.4
eV (0.1 eV), and robust against external strains. The 3D crystals of these two
materials are good layered compounds with very weak inter-layer bonding and are
located near the phase boundary between weak and strong topological insulators,
which pave a new way to future experimental studies on both QSH effect and
topological phase transitions.Comment: 16 pages, 6 figure
Topological fault-tolerance in cluster state quantum computation
We describe a fault-tolerant version of the one-way quantum computer using a
cluster state in three spatial dimensions. Topologically protected quantum
gates are realized by choosing appropriate boundary conditions on the cluster.
We provide equivalence transformations for these boundary conditions that can
be used to simplify fault-tolerant circuits and to derive circuit identities in
a topological manner. The spatial dimensionality of the scheme can be reduced
to two by converting one spatial axis of the cluster into time. The error
threshold is 0.75% for each source in an error model with preparation, gate,
storage and measurement errors. The operational overhead is poly-logarithmic in
the circuit size.Comment: 20 pages, 12 figure
Finite Boolean Algebras for Solid Geometry using Julia's Sparse Arrays
The goal of this paper is to introduce a new method in computer-aided
geometry of solid modeling. We put forth a novel algebraic technique to
evaluate any variadic expression between polyhedral d-solids (d = 2, 3) with
regularized operators of union, intersection, and difference, i.e., any CSG
tree. The result is obtained in three steps: first, by computing an independent
set of generators for the d-space partition induced by the input; then, by
reducing the solid expression to an equivalent logical formula between Boolean
terms made by zeros and ones; and, finally, by evaluating this expression using
bitwise operators. This method is implemented in Julia using sparse arrays. The
computational evaluation of every possible solid expression, usually denoted as
CSG (Constructive Solid Geometry), is reduced to an equivalent logical
expression of a finite set algebra over the cells of a space partition, and
solved by native bitwise operators.Comment: revised version submitted to Computer-Aided Geometric Desig
Cubical Cohomology Ring of 3D Photographs
Cohomology and cohomology ring of three-dimensional (3D) objects are
topological invariants that characterize holes and their relations. Cohomology
ring has been traditionally computed on simplicial complexes. Nevertheless,
cubical complexes deal directly with the voxels in 3D images, no additional
triangulation is necessary, facilitating efficient algorithms for the
computation of topological invariants in the image context. In this paper, we
present formulas to directly compute the cohomology ring of 3D cubical
complexes without making use of any additional triangulation. Starting from a
cubical complex that represents a 3D binary-valued digital picture whose
foreground has one connected component, we compute first the cohomological
information on the boundary of the object, by an incremental
technique; then, using a face reduction algorithm, we compute it on the whole
object; finally, applying the mentioned formulas, the cohomology ring is
computed from such information
Colloidal particles in liquid crystal films and at interfaces
This mini-review discusses the recent contribution of theoretical and
computational physics as well as experimental efforts to the understanding of
the behavior of colloidal particles in confined geometries and at liquid
crystalline interfaces. Theoretical approaches used to study trapping, long-
and short-range interactions, and assembly of solid particles and liquid
inclusions are outlined. As an example, an interaction of a spherical colloidal
particle with a nematic-isotropic interface and a pair interaction potential
between two colloids at this interface are obtained by minimizing the Landau-de
Gennes free energy functional using the finite-element method with adaptive
meshes.Comment: 22 pages, 10 figure
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