Asymptotic of the density of states for the Schrödinger operator with periodic electromagnetic potential

Abstract

For the Schrödinger operator in L2(Rn), n>1, with C∞ periodic electromagnetic potential, we give an asymptotic formula of the integrate density of states of the form N(μ)=anμn/2+O(μ(n−2+ε)/2), ∀ε>0. When n=2, this estimate enables us to prove the finiteness of gaps in the spectrum.