Magnetic Schrödinger operators and landscape functions.

We study localization properties of low-lying eigenfunctions of magnetic Schrödinger operators (− i ∇ − A (x)) 2 ϕ + V (x) ϕ = λ ϕ , where V : Ω → R ≥ 0 is a given potential and A : Ω → R d induces a magnetic field. We extend the Filoche-Mayboroda inequality and prove a refined inequality in the magnetic setting which can predict the points where low-energy eigenfunctions are localized. This result is new even in the case of vanishing magnetic field A ≡ 0 . Numerical examples illustrate the results. [ABSTRACT FROM AUTHOR]