On the Bound States of Magnetic Laplacians on Wedges

0496842 - ÚJF 2019 RIV GB eng J - Článek v odborném periodiku
Exner, Pavel - Lotoreichik, Vladimir - Pérez-Obiol, Axel Castaneda
On the Bound States of Magnetic Laplacians on Wedges.
Reports on Mathematical Physics. Roč. 82, č. 2 (2018), s. 161-185. ISSN 0034-4877. E-ISSN 1879-0674
Grant CEP: GA ČR GA17-01706S; GA ČR(CZ) GA15-04301S
Institucionální podpora: RVO:61389005
Klíčová slova: magnetic Laplacian * homogeneous magnetic field * wedge-type domains * Neumann and Robin boundary conditions * delta-interactions * existence of bound states * min-max principle * test functions * computer-assistance
Obor OECD: Atomic, molecular and chemical physics (physics of atoms and molecules including collision, interaction with radiation, magnetic resonances, Mössbauer effect)
Impakt faktor: 0.989, rok: 2018

This paper is mainly inspired by the conjecture about the existence of bound states for magnetic Neumann Laplacians on planar wedges of any aperture phi is an element of (0,pi). So far, a proof was only obtained for apertures phi less than or similar to 0.511 pi. The conviction in the validity of this conjecture for apertures phi greater than or similar to 0.511 pi mainly relied on numerical computations. In this paper we succeed to prove the existence of bound states for any aperture phi less than or similar to 0.583 pi using a variational argument with suitably chosen test functions. Employing some more involved test functions and combining a variational argument with computer assistance, we extend this interval up to any aperture phi less than or similar to 0.595 pi. Moreover, we analyse the same question for closely related problems concerning magnetic Robin Laplacians on wedges and for magnetic Schrodinger operators in the plane with delta-interactions supported on broken lines.
Trvalý link: http://hdl.handle.net/11104/0289459