Schrödinger evolution on surfaces in 3D contact sub-Riemannian manifolds
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.
math.SP↗