Magnetic Laplacian in sharp three dimensional cones
Spectral Theory
2017-11-23 v2 Analysis of PDEs
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.
Keywords
Cite
@article{arxiv.1505.03033,
title = {Magnetic Laplacian in sharp three dimensional cones},
author = {Virginie Bonnaillie-Noël and Monique Dauge and Nicolas Popoff and Nicolas Raymond},
journal= {arXiv preprint arXiv:1505.03033},
year = {2017}
}