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Symmetry protected topological phases under decoherence
Quantum, 2022We investigate mixed states exhibiting nontrivial topological features, focusing on symmetry-protected topological (SPT) phases under various types of decoherence.
Jong Yeon Lee, Yi-Zhuang You, Cenke Xu
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Triangulating topological spaces
Proceedings of the tenth annual symposium on Computational geometry - SCG '94, 1994Given a subspace [Formula: see text] and a finite set S⊆ℝd, we introduce the Delaunay complex, [Formula: see text], restricted by [Formula: see text]. Its simplices are spanned by subsets T⊆S for which the common intersection of Voronoi cells meets [Formula: see text] in a non-empty set. By the nerve theorem, [Formula: see text] and [Formula: see text]
Herbert Edelsbrunner, Nimish R. Shah
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2006
Publisher Summary This chapter provides an overview of the topological spaces. A topological space (X, τ) is a set X with a topology τ, that is, a collection of subsets of X with the following properties: (1) X ∈ τ, o ∈ τ; (2) if A, B ∈ τ then A ∩ B ∈ τ ; and (3) for any collection {Aα}α, if all Aα ∈ τ , then UαAα ∈ τ .
Elena Deza, Michel-Marie Deza
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Publisher Summary This chapter provides an overview of the topological spaces. A topological space (X, τ) is a set X with a topology τ, that is, a collection of subsets of X with the following properties: (1) X ∈ τ, o ∈ τ; (2) if A, B ∈ τ then A ∩ B ∈ τ ; and (3) for any collection {Aα}α, if all Aα ∈ τ , then UαAα ∈ τ .
Elena Deza, Michel-Marie Deza
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Topology and Topological Spaces
1997We have now seen four different proofs of the Fundamental Theorem of Algebra. The first two were purely analysis, while the second pair involved a wide collection of algebraic ideas. However, we should realize that even in these algebraic proofs we did not totally leave analysis.
Gerhard Rosenberger, Benjamin Fine
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Nature Photonics, 2014
Applying the mathematical concept of topology to the wave-vector space of photonics yields exciting opportunities for creating new states of light with useful properties such as unidirectional propagation and the ability to flow around imperfections. The
Ling Lu, J. Joannopoulos, M. Soljačić
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Applying the mathematical concept of topology to the wave-vector space of photonics yields exciting opportunities for creating new states of light with useful properties such as unidirectional propagation and the ability to flow around imperfections. The
Ling Lu, J. Joannopoulos, M. Soljačić
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Experimental observation of non-Abelian topological acoustic semimetals and their phase transitions
Nature Physics, 2021Topological phases of matter connect mathematical principles to real materials, and may shape future electronic and quantum technologies. So far, this discipline has mostly focused on single-gap topology described by topological invariants such as Chern ...
B. Jiang +7 more
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Observation of a phononic quadrupole topological insulator
Nature, 2017The modern theory of charge polarization in solids is based on a generalization of Berry’s phase. The possibility of the quantization of this phase arising from parallel transport in momentum space is essential to our understanding of systems with ...
M. Serra-Garcia +6 more
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Общенациональный интерактивный энциклопедический портал "Знания", 2022
Alexei Yurievich Zoubov
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Alexei Yurievich Zoubov
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Dynamics of Topological Polarization Singularity in Momentum Space.
Physical Review Letters, 2021Yixuan Zeng +4 more
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