We investigate in the framework of quantum noise theory how striking boundary-sensitivity recently discovered context non-Hermitian (NH) topological phases may be harnessed to devise novel sensors. Specifically, we study a quantum-optical setting coupled modes arranged an array with broken ring geometry that would realize NH phase classical limit. Using methods from quantum-information Gaussian...

Nonlinearities in lattices with topologically nontrivial band structures can give rise to topological solitons, whose properties differ from both conventional lattice solitons and linear boundary states. We show that a Su-Schrieffer-Heeger-type nonlinearity nonreciprocal non-Hermiticity hosts novel oscillatory soliton, which we call end breather. The breather is strongly localized self-induced ...

Abstract This article reviews recent developments in the non-Hermitian skin effect (NHSE), particularly on its rich interplay with topology. The review starts off a pedagogical introduction modified bulk-boundary correspondence, synergy and hybridization of NHSE band topology higher dimensions, as well as, associated complex energy plane such spectral winding graph Following which, emerging top...

A new approach to topological clean-up of 2D meshes is presented. Instead of searching for patterns in a mesh and replacing them as in other methods, the proposed method replaces a region in a mesh only according to the boundary of that region. This simplifies the classification of the different cases, and allows mesh modification over greater regions in the mesh. An algorithm for quadrilateral...

We study algebraic properties of the Brandt λ-extensions of monoids with zero and non-trivial homomorphisms between the Brandt λ-extensions of monoids with zero. We introduce finite, compact topological Brandt λextensions of topological semigroups and countably compact topological Brandt λ-extensions of topological inverse semigroups in the class of topological inverse semigroups and establish ...