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Order-Topological lattices [PDF]

Glasgow Mathematical Journal, 1980
The observation that convergence of real sequences may be defined in terms of limits inferior and limits superior as by means of neighbourhoods in the Euclidean topology leads to the question: for which lattices does order convergence coincide with convergence in the order topology? This problem has been attacked by D. C. Kent [10], A.
Erné, Marcel, Riečanová, Zdenka, Zdenka Riečanová, Marcel Erné   +3 more
core   +4 more sources

Topological lattice actions [PDF]

Journal of High Energy Physics, 2010
38 pages, 12 ...
Bietenholz W., Gerber U., Pepe M., Wiese U.-J.   +3 more
openaire   +5 more sources

Topological protection versus degree of entanglement of two-photon light in photonic topological insulators

Nature Communications, 2021
Topological protection of entangled states is a promising avenue for photonic quantum technologies. Here, Tschernig et al. theoretically analyse the impact of disorder on topological protection of entangled two-photon states in periodic and aperiodic ...
Konrad Tschernig, Álvaro Jimenez-Galán, Demetrios N. Christodoulides, Misha Ivanov, Kurt Busch, Miguel A. Bandres, Armando Perez-Leija   +6 more
doaj   +1 more source

Lattice Operators and Topologies [PDF]

International Journal of Mathematics and Mathematical Sciences, 2009
Working within a complete (not necessarily atomic) Boolean algebra, we use a sublattice to define a topology on that algebra. Our operators generalize complement on a lattice which in turn abstracts the set theoretic operator. Less restricted than those of Banaschewski and Samuel, the operators exhibit some surprising behaviors.
openaire   +2 more sources

Synthetic band-structure engineering in polariton crystals with non-Hermitian topological phases

Nature Communications, 2020
To simulate band structures of solid state materials synthetic lattices are usually generated by optical lattices or by irreversible patterning the system.
L. Pickup, H. Sigurdsson, J. Ruostekoski, P. G. Lagoudakis   +3 more
doaj   +1 more source

Fractionalized topological defects in optical lattices

New Journal of Physics, 2015
Topological objects are interesting topics in various fields of physics ranging from condensed matter physics to the grand unified and superstring theories. Among those, ultracold atoms provide a playground to study the complex topological objects.
Xing-Hai Zhang, Wen-Jun Fan, Jin-Wei Shi, Su-Peng Kou   +3 more
doaj   +1 more source

Finite Simple Graphs and Their Associated Graph Lattices

Theory and Applications of Graphs, 2018
In his 2005 dissertation, Antoine Vella explored combinatorical aspects of finite graphs utilizing a topological space whose open sets are intimately tied to the structure of the graph.
James B. Hart, Brian Frazier
doaj   +1 more source

Manipulating topological valley modes in plasmonic metasurfaces

Nanophotonics, 2020
Coupled light-matter modes supported by plasmonic metasurfaces can be combined with topological principles to yield subwavelength topological valley states of light.
Proctor Matthew, Huidobro Paloma A., Maier Stefan A., Craster Richard V., Makwana Mehul P.   +4 more
doaj   +1 more source

Strongly correlated and topological states in [111] grown transition metal oxide thin films and heterostructures

APL Materials, 2020
We highlight recent advances in the theory, materials fabrication, and experimental characterization of strongly correlated and topological states in [111] oriented transition metal oxide thin films and heterostructures, which are notoriously difficult ...
Jak Chakhalian, Xiaoran Liu, Gregory A. Fiete   +2 more
doaj   +1 more source

HEMI-COMPLEMENTED LATTICES [PDF]

Journal of Algebraic Systems
The notion of hemicomplemented lattices is introduced and some of the properties of these algebras are studied. Some characterization theorems of hemicomplemented lattices are derived with the help of minimal prime D-filters, ideals, and congruences. The
Phaneendra Kumar Ananthapatnayakuni, Sambasiva Rao Mukkamala   +1 more
doaj   +1 more source