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Mathematics > Operator Algebras

arXiv:2305.12026 (math)
[Submitted on 19 May 2023 (v1), last revised 27 Oct 2023 (this version, v2)]

Title:Even spheres as joint spectra of matrix models

Authors:Alexander Cerjan, Terry A. Loring
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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.
Comments: 19 pages, 4 figures
Subjects: Operator Algebras (math.OA); Mesoscale and Nanoscale Physics (cond-mat.mes-hall)
Cite as: arXiv:2305.12026 [math.OA]
  (or arXiv:2305.12026v2 [math.OA] for this version)
  https://doi.org/10.48550/arXiv.2305.12026
Journal reference: Journal of Mathematical Analysis and Applications 531, 127892 (2024)
Related DOI: https://doi.org/10.1016/j.jmaa.2023.127892

Submission history

From: Terry Loring A [view email]
[v1] Fri, 19 May 2023 22:41:07 UTC (263 KB)
[v2] Fri, 27 Oct 2023 22:36:48 UTC (265 KB)
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