Embedding the Grushin Cylinder in ${\bf R}^3$and Schroedinger evolution
| Autor: | Beschastnyi, Ivan, Boscain, Ugo, Cannarsa, Daniele, Pozzoli, Eugenio |
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| Přispěvatelé: | Centro de Investigaçao e Desenvolvimento em Matematica e Aplicaçoes (CIDMA), Universidade de Aveiro, Centre National de la Recherche Scientifique (CNRS), Laboratoire Jacques-Louis Lions (LJLL (UMR_7598)), Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité), Control And GEometry (CaGE ), Inria de Paris, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire Jacques-Louis Lions (LJLL (UMR_7598)), Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité), Department of Mathematics and Statistics [Jyväskylä Univ] (JYU), University of Jyväskylä (JYU), Università degli studi di Bari Aldo Moro = University of Bari Aldo Moro (UNIBA), Academy of Finland, grant 322898 'Sub-Riemannian Geometry via Metric-geometry and Lie-group Theory', STARS Consolidator Grant 2021 'NewSRG' of the University of Padova, PNRR MUR project PE0000023-NQSTI, UIDP/04106/2020, UIDB/04106/2020, ANR-22-CE92-0077,CoRoMo,Contrôle quantique performante des rotations moléculaires -- temps et controllabilité(2022) |
| Jazyk: | angličtina |
| Rok vydání: | 2023 |
| Předmět: |
Mathematics - Functional Analysis
Mathematics - Differential Geometry Grushin Differential Geometry (math.DG) [MATH.MATH-DG]Mathematics [math]/Differential Geometry [math.DG] [MATH.MATH-MP]Mathematics [math]/Mathematical Physics [math-ph] FOS: Mathematics FOS: Physical sciences Mathematical Physics (math-ph) [MATH.MATH-FA]Mathematics [math]/Functional Analysis [math.FA] Mathematical Physics Functional Analysis (math.FA) |
| Popis: | We consider the evolution of a free quantum particle on the Grushin cylinder, under different type of quantizations. In particular we are interested to understand if the particle can cross the singular set, i.e., the set where the structure is not Riemannian. We consider intrinsic and extrinsic quantizations, where the latter are obtained by embedding the Grushin structure isometrically in ${\bf R}^3$ (with singularities). As a byproduct we provide formulas to embed the Grushin cylinder in ${\bf R^3}$ that could be useful for other purposes. Such formulas are not global, but permit to study the embedding arbitrarily close to the singular set. We extend these results to the case of $\alpha $-Grushin cylinders. Comment: 16 pages, 8 figures |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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