Semiclassical analysis for a Schrödinger operator with a U(2) artificial gauge: the periodic case

Abstract : We consider a Schrödinger operator with a Hermitian 2x2 matrix-valued potential which is lattice periodic and can be diagonalized smoothly on the whole $R^n.$ In the case of potential taking its minimum only on the lattice, we prove that the well-known semiclassical asymptotic of first band spectrum for a scalar potential remains valid for our model.
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Abderemane Morame, Francoise Truc. Semiclassical analysis for a Schrödinger operator with a U(2) artificial gauge: the periodic case. Reviews in Mathematical Physics, World Scientific Publishing, 2016, 28 (8), ⟨10.1142/S0129055X16500148⟩. ⟨hal-00936313v2⟩

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