Even spheres as joint spectra of matrix models

Abstract

The Clifford spectrum is a form of joint spectrum for noncommuting matrices. This theory has been applied in photonics, condensed matter and string theory. In applications, the Clifford spectrum can be efficiently approximated using numerical methods, but this only is possible in low dimensional example. Here we examine the higher-dimensional spheres that can arise from theoretical examples. We also describe a constuctive method to generate five real symmetric almost commuting matrices that have a $K$-theoretical obstruction to being close to commuting matrices. For this, we look to matrix models of topological electric circuits.

19 pages, 4 figures

References in corpus (5)

• Classification of topological insulators and superconductors in three spatial dimensions
• Experimental Observation of Berry Phases in Optical Moebius-strip Microcavities
• An operator-based approach to topological photonics
• Quadratic pseudospectrum for identifying localized states
• Revealing Topology in Metals using Experimental Protocols Inspired by $K$-Theory

Cited by in corpus (3)

• Tutorial: Classifying Photonic Topology Using the Spectral Localizer and Numerical $K$-Theory
• Dimensional crossover of class D real-space topological invariants
• Operator Projective Line and Its Transformations