Geometric confinement and dynamical transmission of a quantum particle in Grushin cylinder

16 Mar 2020 Gallone Matteo Michelangeli Alessandro Pozzoli Eugenio

We classify the self-adjoint realisations of the Laplace-Beltrami operator minimally defined on an infinite cylinder equipped with an incomplete Riemannian metric of Grushin type, in the non-trivial class of metrics yielding an infinite deficiency index. Such realisations are naturally interpreted as Hamiltonians governing the geometric confinement of a Schr\"{o}dinger quantum particle away from the singularity, or the dynamical transmission across the singularity... (read more)

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  • DIFFERENTIAL GEOMETRY
  • MATHEMATICAL PHYSICS
  • MATHEMATICAL PHYSICS
  • QUANTUM PHYSICS