Geodesic
Helical magnetic fields and semi-classical asymptotics of the lowest eigenvalue
Documenta mathematica, Tome 28 (2023) no. 4, pp. 857-901

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We study the three-dimensional Neumann magnetic Laplacian in the presence of a semiclassical parameter and a non-uniform magnetic field with constant intensity. We determine a sharp two term asymptotics for the lowest eigenvalue, where the second term involves a quantity related to the magnetic field and the geometry of the domain. In the special case of the unit ball and a helical magnetic field, the concentration takes place on two symmetric points of the unit sphere.
DOI : 10.4171/dm/922
Classification : 35P15, 35Q56
Mots-clés : Magnetic Laplacian, Neumann boundary condition, semi-classical analysis 
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     title = {Helical magnetic fields and semi-classical asymptotics of the lowest eigenvalue},
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Bernard Helffer; Ayman Kachmar. Helical magnetic fields and semi-classical asymptotics of the lowest eigenvalue. Documenta mathematica, Tome 28 (2023) no. 4, pp. 857-901. doi: 10.4171/dm/922

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