JournalsrmiVol. 35, No. 7pp. 2053–2070

Tunnel effect in a shrinking shell enlacing a magnetic field

  • Ayman Kachmar

    Lebanese University, Hadath, Lebanon
  • Nicolas Raymond

    Université d'Angers, France
Tunnel effect in a shrinking shell enlacing a magnetic field cover

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Abstract

Let CC be a smooth planar curve. We assume that CC 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 CC, 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).

Cite this article

Ayman Kachmar, Nicolas Raymond, Tunnel effect in a shrinking shell enlacing a magnetic field. Rev. Mat. Iberoam. 35 (2019), no. 7, pp. 2053–2070

DOI 10.4171/RMI/1110