Abstract
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 Schr\"odinger operator when such sharp cones are involved.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
