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On Geometric Quantum Confinement in Grushin-Like Manifolds

TitleOn Geometric Quantum Confinement in Grushin-Like Manifolds
Publication TypePreprint
2018
AuthorsGallone, M, Michelangeli, A, Pozzoli, E
Document NumberSISSA;36/2018/MATE

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.

http://preprints.sissa.it/handle/1963/35322

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