تقرير
SVD, joint-MVD, Berry phase, and generic loss of rank for a matrix valued function of 2 parameters
| العنوان: | SVD, joint-MVD, Berry phase, and generic loss of rank for a matrix valued function of 2 parameters |
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| المؤلفون: | Dieci, Luca, Pugliese, Alessandro |
| سنة النشر: | 2024 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Rings and Algebras, 15A18, 15A23, 15A99 |
| الوصف: | 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). Comment: 18 pages |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2402.14689 |
| رقم الأكسشن: | edsarx.2402.14689 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |