Accessibility navigation

Spectral analysis and the Aharonov-Bohm\~ effect on certain almost-Riemannian manifold

Boscain, U., Prandi, D. and Seri, M. (2016) Spectral analysis and the Aharonov-Bohm\~ effect on certain almost-Riemannian manifold. Communications in Partial Differential Equations, 41 (1). pp. 32-50. ISSN 0360-5302

Full text not archived in this repository.

It is advisable to refer to the publisher's version if you intend to cite from this work. See Guidance on citing.

To link to this item DOI: 10.1080/03605302.2015.1095766


We study spectral properties of the Laplace-Beltrami operator on two relevant almost-Riemannian manifolds, namely the Grushin structures on the cylinder and on the sphere. This operator contains first order diverging terms caused by the divergence of the volume. We get explicit descriptions of the spectrum and the eigenfunctions. In particular in both cases we get a Weyl's law with leading term Elog E. We then study the drastic effect of Aharonov-Bohm magnetic potentials on the spectral properties. Other generalised Riemannian structures including conic and anti-conic type manifolds are also studied. In this case, the Aharonov-Bohm magnetic potential may affect the self-adjointness of the Laplace-Beltrami operator.

Item Type:Article
Divisions:Faculty of Science > School of Mathematical, Physical and Computational Sciences > Department of Mathematics and Statistics
ID Code:47042

University Staff: Request a correction | Centaur Editors: Update this record

Page navigation