Tunnel effect in a shrinking shell enlacing a magnetic field

• Ayman Kachmar ^[1] ; Nicolas Raymond ^[2]
  1. [1] Lebanese University

     Lebanese University

     Líbano

     
  2. [2] University of Angers

     University of Angers

     Arrondissement d’Angers, Francia

     
• Localización: Revista matemática iberoamericana, ISSN 0213-2230, Vol. 35, Nº 7, 2019, págs. 2053-2070
• Idioma: inglés
• DOI: 10.4171/rmi/1110
• Texto completo no disponible (Saber más ...)
• Resumen

  • 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).