scholarly journals Soft topological lattice wheels

2021 ◽  
pp. 101344
Author(s):  
William Zunker ◽  
Stefano Gonella
Keyword(s):  
Topological Lattice

scholarly journals Vortex states in an acoustic Weyl crystal with a topological lattice defect

2021 ◽  
Vol 12 (1) ◽  
Author(s):  
Qiang Wang ◽  
Yong Ge ◽  
Hong-xiang Sun ◽  
Haoran Xue ◽  
Ding Jia ◽  
...  
Keyword(s):  
Angular Momentum ◽  
Orbital Angular Momentum ◽  
Lattice Defect ◽  
Three Dimensional ◽  
Surface States ◽  
Real Space ◽  
Lattice Defects ◽  
One Dimensional ◽  
Topological Features ◽  
Topological Lattice

AbstractCrystalline materials can host topological lattice defects that are robust against local deformations, and such defects can interact in interesting ways with the topological features of the underlying band structure. We design and implement a three dimensional acoustic Weyl metamaterial hosting robust modes bound to a one-dimensional topological lattice defect. The modes are related to topological features of the bulk bands, and carry nonzero orbital angular momentum locked to the direction of propagation. They span a range of axial wavenumbers defined by the projections of two bulk Weyl points to a one-dimensional subspace, in a manner analogous to the formation of Fermi arc surface states. We use acoustic experiments to probe their dispersion relation, orbital angular momentum locked waveguiding, and ability to emit acoustic vortices into free space. These results point to new possibilities for creating and exploiting topological modes in three-dimensional structures through the interplay between band topology in momentum space and topological lattice defects in real space.

Notes on Locally Compact Connected Topological Lattices

1969 ◽  
Vol 21 ◽  
pp. 1533-1536
Author(s):  
Tae Ho Choe
Keyword(s):  
Lower Bound ◽  
Boolean Algebra ◽  
Upper Bound ◽  
Euclidean Plane ◽  
Locally Compact ◽  
Finite Dimensional ◽  
Topological Lattice ◽  
Topological Boolean Algebra ◽  
Locally Convex ◽  
Totally Disconnected

I t was shown in (2) that if(1) L is a locally compact connected topological lattice and if(2) L is topologically contained in R2, the Euclidean plane, then each compact subset of L has an upper bound and a lower bound in L. I t was also asked whether this result could be proved without assuming condition (2). In this note, we show that this result continues to hold if condition (2) is weakened to: L is finite-dimensional.In (11), it was shown that the centre of a compact topological lattice is totally disconnected. We shall prove t h a t this result is also true even in a locally compact, locally convex topological lattice with 0 and 1. This yields that any locally compact topological Boolean algebra is totally disconnected.

scholarly journals Geometric stability of topological lattice phases

2015 ◽  
Vol 6 (1) ◽  
Author(s):  
T. S. Jackson ◽  
Gunnar Möller ◽  
Rahul Roy
Keyword(s):  
Topological Lattice

scholarly journals TOPOLOGICAL LATTICE MODELS IN FOUR DIMENSIONS

1992 ◽  
Vol 07 (30) ◽  
pp. 2799-2810 ◽  
Author(s):  
HIROSI OOGURI
Keyword(s):  
Partition Function ◽  
Piecewise Linear ◽  
Lattice Models ◽  
Closed Surface ◽  
Statistical Weight ◽  
Four Dimensions ◽  
Angular Momenta ◽  
Topological Lattice ◽  
Wilson Operator ◽  
Dimensional Version

We define a lattice statistical model on a triangulated manifold in four dimensions associated to a group G. When G= SU (2), the statistical weight is constructed from the 15j-symbol as well as the 6j-symbol for recombination of angular momenta, and the model may be regarded as the four-dimensional version of the Ponzano-Regge model. We show that the partition function of the model is invariant under the Alexander moves of the simplicial complex, thus it depends only on the piecewise linear topology of the manifold. For an orientable manifold, the model is related to the so-called BF model. The q-analog of the model is also constructed, and it is argued that its partition function is invariant under the Alexander moves. It is discussed how to realize the 't Hooft operator in these models associated to a closed surface in four dimensions as well as the Wilson operator associated to a closed loop. Correlation functions of these operators in the q-deformed version of the model would define a new type of invariants of knots and links in four dimensions.

scholarly journals Решеточная структура в пространстве ограниченных гомоморфизмов между топологическими решеточно упорядоченными кольцами

2019 ◽  
Author(s):  
O. Zabeti
Keyword(s):  
Lattice Structure ◽  
Bounded Operators ◽  
Topological Ring ◽  
Topological Structures ◽  
Riesz Spaces ◽  
Topological Lattice ◽  
Bounded Group

Suppose X is a topological ring. It is known that there are three classes of bounded group homomorphisms on X whose topological structures make them again topological rings. First, we show that if X is a Hausdorff topological ring, then so are these classes of bounded group homomorphisms on X. Now, assume that X is a locally solid lattice ring. In this paper, our aim is to consider lattice structure on these classes of bounded group homomorphisms more precisely, we show that, under some mild assumptions, they are locally solid lattice rings. In fact, we consider bounded order bounded homomorphisms on X. Then we show that under the assumed topology, they form locally solid lattice rings. For this reason, we need a version of the remarkable RieszKantorovich formulae for order bounded operators in Riesz spaces in terms of order bounded homomorphisms on topological lattice groups.

scholarly journals Topological lattice using multi-frequency radiation

2018 ◽  
Vol 20 (5) ◽  
pp. 055001 ◽  
Author(s):  
Tomas Andrijauskas ◽  
I B Spielman ◽  
Gediminas Juzeliūnas
Keyword(s):  
Topological Lattice ◽  
Frequency Radiation

scholarly journals On locally solid topological lattice groups

2007 ◽  
Vol 57 (3) ◽  
pp. 963-973 ◽  
Author(s):  
Abdul Rahim Khan ◽  
Keith Rowlands
Keyword(s):  
Topological Lattice
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