Quantum particle across Grushin singularity
M Gallone, A Michelangeli - Journal of Physics A: Mathematical …, 2021 - iopscience.iop.org
A class of models is considered for a quantum particle constrained on degenerate
Riemannian manifolds known as Grushin cylinders, and moving freely subject only to the …
Riemannian manifolds known as Grushin cylinders, and moving freely subject only to the …
Weighted spectral cluster bounds and a sharp multiplier theorem for ultraspherical Grushin operators
V Casarino, P Ciatti, A Martini - … Mathematics Research Notices, 2022 - academic.oup.com
We study degenerate elliptic operators of Grushin type on the-dimensional sphere, which
are singular on a-dimensional sphere for some. For these operators we prove a spectral …
are singular on a-dimensional sphere for some. For these operators we prove a spectral …
Quantum Confinement for the Curvature Laplacian −Δ + cK on 2D-Almost-Riemannian Manifolds
Two-dimension almost-Riemannian structures of step 2 are natural generalizations of the
Grushin plane. They are generalized Riemannian structures for which the vectors of a local …
Grushin plane. They are generalized Riemannian structures for which the vectors of a local …
Uniform, localized asymptotics for sub-Riemannian heat kernels and diffusions
RW Neel, L Sacchelli - arXiv preprint arXiv:2012.12888, 2020 - arxiv.org
We show how Molchanov's method provides a systematic approach to determining the small-
time asymptotics of the heat kernel on a sub-Riemannian manifold away from any abnormal …
time asymptotics of the heat kernel on a sub-Riemannian manifold away from any abnormal …