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Article Dans Une Revue Communications in Mathematical Physics Année : 2020

Symmetry results in two-dimensional inequalities for Aharonov-Bohm magnetic fields

Résumé

This paper is devoted to the symmetry and symmetry breaking properties of a two-dimensional magnetic Schrödinger operator involving an Aharonov-Bohm magnetic vector potential. We investigate the symmetry properties of the optimal potential for the corresponding magnetic Keller-Lieb-Thir-ring inequality. We prove that this potential is radially symmetric if the intensity of the magnetic field is below an explicit threshold, while symmetry is broken above a second threshold corresponding to a higher magnetic field. The method relies on the study of the magnetic kinetic energy of the wave function and amounts to study the symmetry properties of the optimal functions in a magnetic Hardy-Sobolev interpolation inequality. We give a quantified range of symmetry by a non-perturbative method. To establish the symmetry breaking range, we exploit the coupling of the phase and of the modulus and also obtain a quantitative result.
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Dates et versions

hal-02003872 , version 1 (01-02-2019)
hal-02003872 , version 2 (12-07-2019)

Identifiants

Citer

Denis Bonheure, Jean Dolbeault, Maria J. Esteban, Ari Laptev, Michael Loss. Symmetry results in two-dimensional inequalities for Aharonov-Bohm magnetic fields. Communications in Mathematical Physics, 2020, 375 (3), pp.2071-2087. ⟨10.1007/s00220-019-03560-y⟩. ⟨hal-02003872v2⟩
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