Schrödinger evolution on surfaces in 3D contact sub-Riemannian manifolds
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arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866915167100469248 |
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| author | Adami, Riccardo Boscain, Ugo Prandi, Dario Tessarolo, Lucia |
| author_facet | Adami, Riccardo Boscain, Ugo Prandi, Dario Tessarolo, Lucia |
| contents | Let $M$ be a 3-dimensional contact sub-Riemannian manifold and $S$ a surface embedded in $M$. Such a surface inherits a field of directions that becomes singular at characteristic points. The integral curves of such field define a characteristic foliation $\mathscr{F}$. In this paper we study the Schrödinger evolution of a particle constrained on $\mathscr{F}$. In particular, we relate the self-adjointness of the Schrödinger operator with a geometric invariant of the foliation. We then classify a special family of its self-adjoint extensions: those that yield disjoint dynamics. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_16186 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Schrödinger evolution on surfaces in 3D contact sub-Riemannian manifolds Adami, Riccardo Boscain, Ugo Prandi, Dario Tessarolo, Lucia Spectral Theory Differential Geometry 53C17, 34B24, 35J10, 47B25, 57K33, 81Q10 Let $M$ be a 3-dimensional contact sub-Riemannian manifold and $S$ a surface embedded in $M$. Such a surface inherits a field of directions that becomes singular at characteristic points. The integral curves of such field define a characteristic foliation $\mathscr{F}$. In this paper we study the Schrödinger evolution of a particle constrained on $\mathscr{F}$. In particular, we relate the self-adjointness of the Schrödinger operator with a geometric invariant of the foliation. We then classify a special family of its self-adjoint extensions: those that yield disjoint dynamics. |
| title | Schrödinger evolution on surfaces in 3D contact sub-Riemannian manifolds |
| topic | Spectral Theory Differential Geometry 53C17, 34B24, 35J10, 47B25, 57K33, 81Q10 |
| url | https://arxiv.org/abs/2502.16186 |