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arXiv · 2502.16186

Schr\"odinger evolution on surfaces in 3D contact sub-Riemannian manifolds

Riccardo Adami·Ugo Boscain·Dario Prandi·Lucia Tessarolo
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Abstract

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 Schr\"odinger evolution of a particle constrained on $\mathscr{F}$. In particular, we relate the self-adjointness of the Schr\"odinger operator with a geometric invariant of the foliation. We then classify a special family of its self-adjoint extensions: those that yield disjoint dynamics.

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Riccardo Adami, Ugo Boscain, Dario Prandi, Lucia Tessarolo. 2025-02-22. Schr\"odinger evolution on surfaces in 3D contact sub-Riemannian manifolds. https://arxiv.org/abs/2502.16186

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