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This paper is devoted to semiclassical tunneling estimates induced on the circle by a double well electric potential in the case when a magnetic field is added. When the two electric wells are connected by two geodesics for the Agmon distance, we highlight an oscillating factor (related to the circulation of the magnetic field) in the splitting estimate of the first two eigenvalues.
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Virginie Bonnaillie-Noël, Frédéric Hérau, Nicolas Raymond, Semiclassical tunneling and magnetic flux effects on the circle. J. Spectr. Theory 7 (2017), no. 3, pp. 771–796