Related papers: Topological hyperbolic lattices
Band topology has been studied as a design principle of realizing robust boundary modes. Here, by exploring non-Hermitian topology, we propose a three-dimensional topological laser that amplifies surface modes. The topological surface laser…
In this work we study topological properties of the one-dimensional Creutz ladder model with different non-Hermitian asymmetric hoppings and on-site imaginary potentials, and obtain phase diagrams regarding the presence and absence of an…
This survey reviews hyperbolic graph embedding models, and evaluate them on anomaly detection, highlighting their advantages over Euclidean methods in capturing complex structures. Evaluating models like \textit{HGCAE},…
We propose a nanophotonic platform for topological quantum optics. Our system is composed of a two-dimensional lattice of non-linear quantum emitters with optical transitions embedded in a photonic crystal slab. The emitters interact…
We study the geometry of hyperbolic cone surfaces, possibly with cusps or geodesic boundaries. We prove that any hyperbolic cone structure on a surface of non-exceptional type is determined up to isotopy by the geodesic lengths of a finite…
Object detection, for the most part, has been formulated in the euclidean space, where euclidean or spherical geodesic distances measure the similarity of an image region to an object class prototype. In this work, we study whether a…
Various topological techniques and tools have been applied to neural networks in terms of network complexity, explainability, and performance. One fundamental assumption of this line of research is the existence of a global (Euclidean)…
Photonic topological phases offering unprecedented manipulation of electromagnetic waves have attracted much research interest which, however, have been mostly restricted to a single band gap. Here, we report on the experimental discovery…
We show that Bose-Einstein condensates in optical lattices with broken time-reversal symmetry can support chiral edge modes originating from nontrivial bulk excitation band topology. To be specific, we analyze a Bose-Hubbard extension of…
Gyroscopic metamaterials --- mechanical structures composed of interacting spinning tops --- have recently been found to support one-way topological edge excitations. In these structures, the time reversal symmetry breaking that enables…
Wave functions on periodic lattices are commonly described by Bloch band theory. Besides Abelian Bloch states labeled by a momentum vector, hyperbolic lattices support non-Abelian Bloch states that have so far eluded analytical treatments.…
Non-Hermitian topological photonics is of great interest in bridging topological matter with gain/dissipation engineering in optics. A key problem in this direction is the interplay between the effective gauge potential and the…
Within the expanding field of non-Hermitian physics, non-Hermitian pumping has emerged as a key phenomenon, epitomized through the skin effect via extensive boundary mode accumulation modifying the conventional Bloch picture. Beyond…
The Laplace operator encodes the behavior of physical systems at vastly different scales, describing heat flow, fluids, as well as electric, gravitational, and quantum fields. A key input for the Laplace equation is the curvature of space.…
We derive the full spectrum of decorated Cayley trees that constitute tree analogs of selected two-dimensional Euclidean lattices; namely of the Lieb, the double Lieb, the kagome, and the star lattice. The common feature of these Euclidean…
We prove that general helices in Euclidean space for Killing vector fields associated to rotations are helices, that is, curves with constant curvature and constant torsion. In hyperbolic space $\h^3$, we obtain the parametrization of…
Solids built out of active components can exhibit non-reciprocal elastic coefficients that give rise to non-Hermitian wave phenomena. Here, we investigate non-Hermitian effects present at the boundary of two-dimensional active elastic media…
How can we convince students, who have mainly learned to follow given mathematical rules, that mathematics can also be fascinating, creative, and beautiful? In this paper I discuss different ways of introducing non-Euclidean geometry to…
We present a framework to systematically address topological phases when finer partitionings of bands are taken into account, rather than only considering the two subspaces spanned by valence and conduction bands. Focusing on…
The past few years have seen a revived interest in quantum geometrical characterizations of band structures due to the rapid development of topological insulators and semi-metals. Although the metric tensor has been connected to many…