Spectral transitions for Aharonov-Bohm Laplacians on conical layers

0522298 - ÚJF 2020 RIV GB eng J - Journal Article
Krejčiřík, D. - Lotoreichik, Vladimir - Ourmieres-Bonafos, T.
Spectral transitions for Aharonov-Bohm Laplacians on conical layers.
Proceedings of the Royal Society of Edinburgh. A - Mathematics. Roč. 149, č. 6 (2019), s. 1663-1687. ISSN 0308-2105. E-ISSN 1473-7124
Institutional support: RVO:61389005
Keywords : conical geometries * existenceof bound states * quantum layers * Schrödinger operator * spectral asymptotics
OECD category: Atomic, molecular and chemical physics (physics of atoms and molecules including collision, interaction with radiation, magnetic resonances, Mössbauer effect)
Impact factor: 1.009, year: 2019
Method of publishing: Limited access
https://doi.org/10.1017/prm.2018.64

We consider the Laplace operator in a tubular neighbourhood of a conical surface of revolution, subject to an Aharonov-Bohm magnetic field supported on the axis of symmetry and Dirichlet boundary conditions on the boundary of the domain. We show that there exists a critical total magnetic flux depending on the aperture of the conical surface for which the system undergoes an abrupt spectral transition from infinitely many eigenvalues below the essential spectrum to an empty discrete spectrum. For the critical flux, we establish a Hardy-type inequality. In the regime with an infinite discrete spectrum, we obtain sharp spectral asymptotics with a refined estimate of the remainder and investigate the dependence of the eigenvalues on the aperture of the surface and the flux of the magnetic field.
Permanent Link: http://hdl.handle.net/11104/0306810