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.
On geometric quantum confinement in Grushin-type manifolds / M. Gallone, A. Michelangeli, E. Pozzoli. - In: ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK. - ISSN 0044-2275. - 70:6(2019 Dec), pp. 158.1-158.17. [10.1007/s00033-019-1203-2]
On geometric quantum confinement in Grushin-type manifolds
M. Gallone
;
2019
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.
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