Revista Matemática Iberoamericana
Full-Text PDF (319 KB) | Metadata | Table of Contents | RMI summary
Published online: 2019-07-30
Tunnel effect in a shrinking shell enlacing a magnetic fieldAyman Kachmar and Nicolas Raymond (1) Lebanese University, Hadath, Lebanon
(2) Université d'Angers, France
Let $C$ be a smooth planar curve. We assume that $C$ is simple, closed, smooth, symmetric with respect to an axis and its curvature attains its minimum at exactly two points away from the axis of symmetry. In a tubular neighborhood about $C$, we study the Laplace operator with a magnetic flux and mixed boundary conditions. As the thickness of the domain tends to 0, we establish an explicit asymptotic formula for the splitting of the first two eigenvalues (tunneling effect).
Keywords: Tunnel effect, semiclassical analysis, magnetic field, shell
Kachmar Ayman, Raymond Nicolas: Tunnel effect in a shrinking shell enlacing a magnetic field. Rev. Mat. Iberoam. 35 (2019), 2053-2070. doi: 10.4171/rmi/1110