SVD, joint-MVD, Berry phase, and generic loss of rank for a matrix valued function of 2 parameters
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866911128404099072 |
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| author | Dieci, Luca Pugliese, Alessandro |
| author_facet | Dieci, Luca Pugliese, Alessandro |
| contents | In this work we consider generic losses of rank for complex valued matrix functions depending on two parameters. We give theoretical results that characterize parameter regions where these losses of rank occur. Our main results consist in showing how following an appropriate smooth SVD along a closed loop it is possible to monitor the Berry phases accrued by the singular vectors to decide if -- inside the loop -- there are parameter values where a loss of rank takes place. It will be needed to use a new construction of a smooth SVD, which we call the "joint-MVD" (minimum variation decomposition). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_14689 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | SVD, joint-MVD, Berry phase, and generic loss of rank for a matrix valued function of 2 parameters Dieci, Luca Pugliese, Alessandro Rings and Algebras 15A18, 15A23, 15A99 In this work we consider generic losses of rank for complex valued matrix functions depending on two parameters. We give theoretical results that characterize parameter regions where these losses of rank occur. Our main results consist in showing how following an appropriate smooth SVD along a closed loop it is possible to monitor the Berry phases accrued by the singular vectors to decide if -- inside the loop -- there are parameter values where a loss of rank takes place. It will be needed to use a new construction of a smooth SVD, which we call the "joint-MVD" (minimum variation decomposition). |
| title | SVD, joint-MVD, Berry phase, and generic loss of rank for a matrix valued function of 2 parameters |
| topic | Rings and Algebras 15A18, 15A23, 15A99 |
| url | https://arxiv.org/abs/2402.14689 |