Revista Matemática Iberoamericana

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Volume 35, Issue 7, 2019, pp. 2053–2070
DOI: 10.4171/rmi/1110

Published online: 2019-07-30

Tunnel effect in a shrinking shell enlacing a magnetic field

Ayman Kachmar[1] and Nicolas Raymond[2]

(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