On Geometric Quantum Confinement in Grushin-type Manifolds
Differential Geometry
2019-10-14 v2 Mathematical Physics
math.MP
Spectral Theory
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.
Cite
@article{arxiv.1809.06805,
title = {On Geometric Quantum Confinement in Grushin-type Manifolds},
author = {Matteo Gallone and Alessandro Michelangeli and Eugenio Pozzoli},
journal= {arXiv preprint arXiv:1809.06805},
year = {2019}
}
Comments
16 pages, 2 figures