Tunneling effect in two dimensions with vanishing magnetic fields
Khaled Abou Alfa
Université de Nantes, Nantes Cedex 3, France
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Abstract
In this paper, we consider the semiclassical 2D magnetic Schrödinger operator in the case where the magnetic field vanishes along a smooth closed curve. Assuming that this curve has an axis of symmetry, we prove that semiclassical tunneling occurs. The main result is an expression of the splitting of the first two eigenvalues and an explicit tunneling formula.
Cite this article
Khaled Abou Alfa, Tunneling effect in two dimensions with vanishing magnetic fields. J. Spectr. Theory 14 (2024), no. 3, pp. 837–889
DOI 10.4171/JST/516