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

Abderemane Morame (1) , Francoise Truc (2)

1 LMJL - Laboratoire de Mathématiques Jean Leray
2 IF - Institut Fourier

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.

Keywords: magnetic field; semiclassical asymptotic; periodic potential; spectrum; eigenvalues; Schrodinger operator; BKW method; width of the first band; magnetic field.

Domains: Mathematical Physics [math-ph]

Abderemane Morame, Francoise Truc. Semiclassical analysis for a Schrödinger operator with a U(2) artificial gauge: the periodic case. Reviews in Mathematical Physics, 2016, 28 (8), ⟨10.1142/S0129055X16500148⟩. ⟨hal-00936313v2⟩