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DC Field | Value | Language |
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dc.contributor.author | Beschastnyi, Ivan | pt_PT |
dc.contributor.author | Boscain, Ugo | pt_PT |
dc.contributor.author | Pozzoli, Eugenio | pt_PT |
dc.date.accessioned | 2023-02-09T18:07:46Z | - |
dc.date.available | 2023-02-09T18:07:46Z | - |
dc.date.issued | 2021-08-06 | - |
dc.identifier.issn | 0926-2601 | pt_PT |
dc.identifier.uri | http://hdl.handle.net/10773/36276 | - |
dc.description.abstract | Two-dimension almost-Riemannian structures of step 2 are natural generalizations of the Grushin plane. They are generalized Riemannian structures for which the vectors of a local orthonormal frame can become parallel. Under the 2-step assumption the singular set $Z$, where the structure is not Riemannian, is a 1D embedded submanifold. While approaching the singular set, all Riemannian quantities diverge. A remarkable property of these structures is that the geodesics can cross the singular set without singularities, but the heat and the solution of the Schrödinger equation (with the Laplace-Beltrami operator $\Delta$) cannot. This is due to the fact that (under a natural compactness hypothesis), the Laplace-Beltrami operator is essentially self-adjoint on a connected component of the manifold without the singular set. In the literature such phenomenon is called quantum confinement. In this paper we study the self-adjointness of the curvature Laplacian, namely $-\Delta+cK$, for $c\in(0,1/2)$ (here $K$ is the Gaussian curvature), which originates in coordinate-free quantization procedures (as for instance in path-integral or covariant Weyl quantization). We prove that there is no quantum confinement for this type of operators. | pt_PT |
dc.language.iso | eng | pt_PT |
dc.publisher | Springer | pt_PT |
dc.relation | info:eu-repo/grantAgreement/EC/H2020/765267/EU | pt_PT |
dc.relation | SRGI ANR-15-CE40-0018 | pt_PT |
dc.relation | Quaco ANR-17-CE40-0007-01 | pt_PT |
dc.rights | openAccess | pt_PT |
dc.subject | Grushin plane | pt_PT |
dc.subject | Quantum confinement | pt_PT |
dc.subject | Almost-Riemannian manifolds | pt_PT |
dc.subject | Coordinate-free quantization procedures | pt_PT |
dc.subject | Self-adjointness of the Laplacian | pt_PT |
dc.subject | Inverse square potential | pt_PT |
dc.title | Quantum confinement for the curvature Laplacian $-Δ+cK$ on 2D-almost-Riemannian manifolds | pt_PT |
dc.type | article | pt_PT |
dc.description.version | published | pt_PT |
dc.peerreviewed | yes | pt_PT |
degois.publication.title | Potential Analysis | pt_PT |
dc.identifier.doi | 10.1007/s11118-021-09946-9 | pt_PT |
dc.identifier.essn | 1572-929X | pt_PT |
Appears in Collections: | CIDMA - Artigos AGG - Artigos DMat - Artigos |
Files in This Item:
File | Description | Size | Format | |
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2011.03300[1].pdf | 307.6 kB | Adobe PDF | View/Open |
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