Results 21 to 30 of about 565,556 (249)
Topological Boundaries of Unitary Representations [PDF]
International Mathematics Research Notices, 2020 AbstractWe introduce and study a generalization of the notion of the Furstenberg boundary of a discrete group $\Gamma $ to the setting of a general unitary representation $\pi : \Gamma \to B(\mathcal H_\pi )$. This space, which we call the “Furstenberg–Hamana boundary” (or "FH-boundary") of the pair $(\Gamma , \pi )$, is a $\Gamma $-invariant subspace ...
Alex Bearden, Mehrdad Kalantar
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Boundary degeneracy of topological order [PDF]
Physical Review B, 2015 We introduce the concept of boundary degeneracy of topologically ordered states on a compact orientable spatial manifold with boundaries, and emphasize that the boundary degeneracy provides richer information than the bulk degeneracy. Beyond the bulk-edge correspondence, we find the ground state degeneracy of the fully gapped edge modes depends on ...
Xiao-Gang Wen +4 more
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Topological boundaries of covariant representations
MATHEMATICA SCANDINAVICA, 2023 We associate a boundary $\mathcal B_{\pi ,u}$ to each covariant representation $(\pi ,u,H)$ of a $C^*$-dynamical system $(G,A,\alpha )$ and study the action of $G$ on $\mathcal B_{\pi ,u}$ and its amenability properties. We relate rigidity properties of traces on the associated crossed product $C^*$-algebra to faithfulness of the action of the group on
Amini, Massoud, Zavar, Sajad
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Topological inference of manifolds with boundary
Computational Geometry, 2020 Given a set of data points sampled from some underlying space, there are two important challenges in geometric and topological data analysis when dealing with sampled data: reconstruction -- how to assemble discrete samples into global structures, and inference -- how to extract geometric and topological information from data that are high-dimensional,
Bei Wang, Yuan Wang
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Extrinsic topology of Floquet anomalous boundary states in quantum walks [PDF]
Phys. Rev. B 105, 094306 (2022), 2021 Bulk-boundary correspondence is a fundamental principle for topological phases where bulk topology determines gapless boundary states. On the other hand, it has been known that corner or hinge modes in higher order topological insulators may appear due to "extrinsic" topology of the boundaries even when the bulk topological numbers are trivial. In this
arxiv +1 more source
Induced Topological Phases at the Boundary of 3D Topological Superconductors [PDF]
Physical Review Letters, 2015 We present tight-binding models of 3D topological superconductors in class DIII that support a variety of winding numbers. We show that gapless Majorana surface states emerge at their boundary in agreement with the bulk-boundary correspondence.
Peter E. Finch +3 more
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Grain-boundary topological phase transitions [PDF]
Proceedings of the National Academy of Sciences, 2020 Significance We reveal the existence of a topological phase transition (Kosterlitz–Thouless type) in grain boundaries (GBs)—important internal surfaces in crystalline materials. GB dynamics are controlled by the formation/migration of line defects (disconnections) with dislocation and step character. Below the GB KT transition, disconnections
Kongtao Chen +2 more
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Evidence of topological boundary modes with topological nodal-point superconductivity [PDF]
Nature Physics, 2021 Raw data of the main text figures. The files can be opened using either MATLAB (*.fig) or Gwyddion (*.gwy).
Haim Beidenkopf +13 more
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Liouvillian skin effect in an exactly solvable model
Physical Review Research, 2022 The interplay between dissipation, topology, and sensitivity to boundary conditions has recently attracted tremendous amounts of attention at the level of effective non-Hermitian descriptions.
Fan Yang +2 more
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Non-Hermitian boundary spectral winding [PDF]
Phys. Rev. B 107, L161404 (2023), 2022 Spectral winding of complex eigenenergies represents a topological aspect unique in non-Hermitian systems, which vanishes in one-dimensional (1D) systems under the open boundary conditions (OBC). In this work, we discover a boundary spectral winding in two-dimensional non-Hermitian systems under the OBC, originating from the interplay between Hermitian
arxiv +1 more source