Magnetic Laplacian in sharp three dimensional cones
Idioma
en
Chapitre d'ouvrage
Este ítem está publicado en
Operator Theory Advances and Application, Operator Theory Advances and Application. 2016, vol. 254, p. 37-56
Birkhäuser/Springer
Resumen en inglés
The core result of this paper is an upper bound for the ground state energyof the magnetic Laplacian with constant magnetic field on cones that are contained in ahalf-space. This bound involves a weighted norm of the ...Leer más >
The core result of this paper is an upper bound for the ground state energyof the magnetic Laplacian with constant magnetic field on cones that are contained in ahalf-space. This bound involves a weighted norm of the magnetic field related to momentson a plane section of the cone. When the cone is sharp, i.e. when its section is small, thisupper bound tends to 0. A lower bound on the essential spectrum is proved for familiesof sharp cones, implying that if the section is small enough the ground state energy is aneigenvalue. This circumstance produces corner concentration in the semi-classical limit forthe magnetic Schrödinger operator when such sharp cones are involved.< Leer menos
Proyecto ANR
Opérateurs non-autoadjoints, analyse semiclassique et problèmes d'évolution - ANR-11-BS01-0019
Centre de Mathématiques Henri Lebesgue : fondements, interactions, applications et Formation - ANR-11-LABX-0020
Centre de Mathématiques Henri Lebesgue : fondements, interactions, applications et Formation - ANR-11-LABX-0020
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