We proposed a framework for the topological classification of non-Hermitian systems. Different from previous $K$-theoretical approaches, our approach is homotopy classification, which enables us to see more invariants. Specifically, we considered systems with separable band structures. found that whole set decomposed into several sectors based on braiding energy levels and characterized by some...

[A] M. Svensson, On holomorphic harmonic morphisms, Manuscripta Math. 107 (2002), 1–13. [B] M. Svensson, Harmonic morphisms from even-dimensional hyperbolic spaces, Math. Scand. 92 (2003), 246–260. [C] M. Svensson, Holomorphic foliations, harmonic morphisms and the Walczak formula, J. London Math. Soc. 68 (2003), 781–794. [D] M. Svensson, Harmonic morphisms in Hermitian geometry, J. Reine Angew...

In this note, we study the notion of structured pseudospectra. We prove that for Toeplitz, circulant and symmetric structures, the structured pseudospectrum equals the unstructured pseudospectrum. We show that this is false for Hermitian and skew-Hermitian structures. We generalize the result to pseudospectra of matrix polynomials. Indeed, we prove that the structured pseudospectrum equals the ...

We introduce T-duality invariant versions of D-branes in doubled geometry using a global covariant framework based on para-Hermitian and metric algebroids. define as conformal boundary conditions for the open string version Born sigma-model, where they are given by maximally isotropic vector bundles which do not generally admit standard geometric picture terms submanifolds. When reduced to conv...

This thesis incorporates the concept of light propagation in non-Hermitian media. We use the waveguide arrays and one dimensional photonic crystals as the frameworks for our investigations. The notion of non-Hermiticity is implemented into these structures by considering the fact that the electromagnetic parameters of an optical medium can contain imaginary components. These imaginary component...

In this article, we consider the almost Hermitian structure on TM induced by a pair of a metric and an affine connection on M . We find the conditions under which TM admits almost Kähler structures, Kähler structures and Einstein metrics, respectively. Moreover, we give two examples of Kähler-Einstein structures on TM . 2000 Mathematics Subject Classification: 53C55, 53C15, 53C25.