On Geometric Quantum Confinement in Grushin-Like Manifolds
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Date
2018-09
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Abstract
We study the problem of so-called geometric quantum confinement in a class of two-dimensional incomplete Riemannian manifold with metric of Grushin type. We employ a constant-fibre direct integral scheme, in combination with Weyl's analysis in each fibre, thus fully characterising the regimes of presence and absence of essential self-adjointness of the associated Laplace-Beltrami operator.
Description
16 pages
Keywords
Geometric quantum confinement, Grushin manifold, geodesically (in)complete Riemannian manifold, Laplace-Beltrami operator, almost-Riemannian structure, self-adjoint operators in Hilbert space, Weyl's limit-point limit-circle criterion, constant-fibre direct integral.