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1. Tunneling effect in two dimensions with vanishing magnetic fields

Author

Alfa, Khaled Abou

Subjects
Mathematics - Spectral Theory, Quantum Physics, FOS: Mathematics, FOS: Physical sciences, Mathematical Physics (math-ph), Quantum Physics (quant-ph), Spectral Theory (math.SP), Mathematical Physics
Abstract

In this paper, we consider the semiclassical 2D magnetic Schr{\"o}dinger 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 semi-classical tunneling occurs. The main result is an expression the splitting of the first two eigenvalues and an explicit tunneling formula.

Published
2022
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