NDLI: Spectral Analysis of Magnetic Laplacians on Conformally Cusp Manifolds

Content Provider	Springer Nature Link
Author	Golénia, Sylvain Moroianu, Sergiu
Copyright Year	2008
Abstract	We consider an open manifold which is the interior of a compact manifold with boundary. Assuming gauge invariance, we classify magnetic fields with compact support into being trapping or non-trapping. We study spectral properties of the associated magnetic Laplacian for a class of Riemannian metrics which includes complete hyperbolic metrics of finite volume. When B is non-trapping, the magnetic Laplacian has nonempty essential spectrum. Using Mourre theory, we show the absence of singular continuous spectrum and the local finiteness of the point spectrum. When B is trapping, the spectrum is discrete and obeys the Weyl law. The existence of trapping magnetic fields with compact support depends on cohomological conditions, indicating a new and very strong long-range effect.In the non-gauge invariant case, we exhibit a strong Aharonov–Bohm effect. On hyperbolic surfaces with at least two cusps, we show that the magnetic Laplacian associated to every magnetic field with compact support has purely discrete spectrum for some choices of the vector potential, while other choices lead to a situation of limiting absorption principle.We also study perturbations of the metric. We show that in the Mourre theory it is not necessary to require a decay of the derivatives of the perturbation. This very singular perturbation is then brought closer to the perturbation of a potential.
Starting Page	131
Ending Page	179
Page Count	49
File Format	PDF
ISSN	14240637
Journal	Annales Henri Poincaré
Volume Number	9
Issue Number	1
e-ISSN	14240661
Language	English
Publisher	SP Birkhäuser Verlag Basel
Publisher Date	2008-01-30
Publisher Place	Basel
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Elementary Particles, Quantum Field Theory Relativity and Cosmology Mathematical Methods in Physics Quantum Physics Dynamical Systems and Ergodic Theory Mathematical and Computational Physics
Content Type	Text
Resource Type	Article
Subject	Statistical and Nonlinear Physics Nuclear and High Energy Physics Mathematical Physics

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