We revisit the question of Peierls substitution for periodic lattice models in the case of weak and slowly variable magnetic field perturbations. We show that up to a first order error in the strength of the magnetic field perturbation, the magnetic band Hamiltonian is iso-spectral with the Weyl quantization of a minimally coupled periodic symbol. This is joint work with Radu Purice (Bucharest).

Slides

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