Purely magnetic tunneling effect in two dimensions

• 成果类型: Article
• 署名作者: Bonnaillie-Noel, Virginie; Herau, Frederic; Raymond, Nicolas
• 署名单位: Centre National de la Recherche Scientifique (CNRS); Universite PSL; Ecole Normale Superieure (ENS); Centre National de la Recherche Scientifique (CNRS); Nantes Universite; Universite d'Angers
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-021-01073-x
• 发表日期: 2022
• 页码: 745-793
• 关键词: low-lying eigenvalues; semi-classical limit; multiple wells; semiclassical analysis; schrodinger-operator; mechanics

摘要

The magnetic Schrodinger operator, with Neumann boundary condition, on a smooth, bounded, and simply connected domain Omega of the Euclidean plane is considered in the semiclassical limit. When Omega has a symmetry axis, the semiclassical splitting of the first two eigenvalues is analyzed. The first explicit tunneling formula in a pure magnetic field is established. The analysis is based on a pseudo-differential reduction to the boundary and the proof of the first known optimal purely magnetic Agmon estimates.