Quantum confinement on non-complete Riemannian manifolds

DOI10.4171/JST/226zbMath1415.58021arXiv1609.01724WikidataQ115212112 ScholiaQ115212112MaRDI QIDQ1624161

Dario Prandi, Luca Rizzi, Marcello Seri

Publication date: 15 November 2018

Published in: Journal of Spectral Theory (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1609.01724

zbMATH Keywords

Schrödinger operatorsalmost-Riemannian geometryquantum completeness

Mathematics Subject Classification ID

Spectral problems; spectral geometry; scattering theory on manifolds (58J50) Linear symmetric and selfadjoint operators (unbounded) (47B25) PDEs in connection with quantum mechanics (35Q40) Selfadjoint operator theory in quantum theory, including spectral analysis (81Q10) Schrödinger operator, Schrödinger equation (35J10) Methods of global Riemannian geometry, including PDE methods; curvature restrictions (53C21)

Related Items (19)

Self-adjointness, \(m\)-accretivity, and separability for perturbations of Laplacian and bi-Laplacian on Riemannian manifolds ⋮ Drift-diffusion equations on domains in \(\mathbb{R}^d\): essential self-adjointness and stochastic completeness ⋮ Heat content asymptotics for sub-Riemannian manifolds ⋮ Inequalities and separation for covariant Schrödinger operators ⋮ Product formulas and convolutions for Laplace-Beltrami operators on product spaces: beyond the trivial case ⋮ Self‐adjointness of non‐semibounded covariant Schrödinger operators on Riemannian manifolds ⋮ Quantum geometric confinement and dynamical transmission in Grushin cylinder ⋮ Mini-workshop: Zero-range and point-like singular perturbations: for a spillover to analysis, PDE and differential geometry. Abstracts from the mini-workshop held October 2--8, 2022 ⋮ Heat kernel bounds and Ricci curvature for Lipschitz manifolds ⋮ Quantum confinement for the curvature Laplacian \(- \Delta + cK\) on 2D-almost-Riemannian manifolds ⋮ Weyl's law for singular Riemannian manifolds ⋮ Closure of the Laplace-Beltrami operator on 2D almost-Riemannian manifolds and semi-Fredholm properties of differential operators on Lie manifolds ⋮ Almost-Riemannian manifolds do not satisfy the curvature-dimension condition ⋮ Essential self-adjointness of symmetric first-order differential systems and confinement of Dirac particles on bounded domains in \({\mathbb{R}}^d\) ⋮ On geometric quantum confinement in Grushin-type manifolds ⋮ Point interactions for 3D sub-Laplacians ⋮ On essential self-adjointness for first order differential operators on domains in \(\mathbb{R}^d\) ⋮ On the essential self-adjointness of singular sub-Laplacians ⋮ Quantum particle across Grushin singularity ^*

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