Tunnel effect in a shrinking shell enlacing a magnetic field | Zendy

Ayman Kachmar | Zendy; Nicolas Raymond | Zendy

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Tunnel effect in a shrinking shell enlacing a magnetic field

Author(s) -

Ayman Kachmar,

Nicolas Raymond

Publication year - 2019

Publication title -

revista matemática iberoamericana

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.569

H-Index - 52

eISSN - 2235-0616

pISSN - 0213-2230

DOI - 10.4171/rmi/1110

Subject(s) - shell (structure) , resizing , condensed matter physics , field (mathematics) , materials science , physics , business , composite material , mathematics , international trade , european union , pure mathematics

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).

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