Geometric phase and holonomy in the space of 2-by-2 symmetric operators Article Swipe
Jakub Rondomanski
,
José D. Cojal González
,
Jürgen P. Rabe
,
Carlos‐Andres Palma
,
Konrad Polthier
·
YOU?
·
· 2024
· Open Access
·
· DOI: https://doi.org/10.48550/arxiv.2411.15038
YOU?
·
· 2024
· Open Access
·
· DOI: https://doi.org/10.48550/arxiv.2411.15038
We present a non-trivial metric tensor field on the space of 2-by-2 real-valued, symmetric matrices whose Levi-Civita connection renders frames of eigenvectors parallel. This results in fundamental reimagining of the space of symmetric matrices as a curved manifold (rather than a flat vector space) and reduces the computation of eigenvectors of one-parameter-families of matrices to a single computation of eigenvectors at an initial point, while the rest are obtained by the parallel transport ODE. Our work has important applications to vibrations of physical systems whose topology is directly explained by the non-trivial holonomy of the spaces of symmetric matrices.
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Metadata
- Type
- preprint
- Language
- en
- Landing Page
- http://arxiv.org/abs/2411.15038
- https://arxiv.org/pdf/2411.15038
- OA Status
- green
- Cited By
- 5
- Related Works
- 10
- OpenAlex ID
- https://openalex.org/W4404987564
All OpenAlex metadata
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https://openalex.org/W4404987564Canonical identifier for this work in OpenAlex
- DOI
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https://doi.org/10.48550/arxiv.2411.15038Digital Object Identifier
- Title
-
Geometric phase and holonomy in the space of 2-by-2 symmetric operatorsWork title
- Type
-
preprintOpenAlex work type
- Language
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enPrimary language
- Publication year
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2024Year of publication
- Publication date
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2024-11-22Full publication date if available
- Authors
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Jakub Rondomanski, José D. Cojal González, Jürgen P. Rabe, Carlos‐Andres Palma, Konrad PolthierList of authors in order
- Landing page
-
https://arxiv.org/abs/2411.15038Publisher landing page
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https://arxiv.org/pdf/2411.15038Direct link to full text PDF
- Open access
-
YesWhether a free full text is available
- OA status
-
greenOpen access status per OpenAlex
- OA URL
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https://arxiv.org/pdf/2411.15038Direct OA link when available
- Concepts
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Holonomy, Mathematics, Pure mathematics, Phase (matter), Space (punctuation), Geometric phase, Mathematical analysis, Computer science, Physics, Quantum mechanics, Operating systemTop concepts (fields/topics) attached by OpenAlex
- Cited by
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5Total citation count in OpenAlex
- Citations by year (recent)
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2025: 3, 2024: 1, 2023: 1Per-year citation counts (last 5 years)
- Related works (count)
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10Other works algorithmically related by OpenAlex
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