Effective Mass Theorems with Bloch Modes Crossings

Abstract We study a Schrödinger equation modeling the dynamics of an electron in crystal asymptotic regime small wave-length comparable to characteristic scale crystal. Using Floquet Bloch decomposition, we obtain description limit time averaged energy densities. make rather general assumption assuming that initial data are uniformly bounded high order Sobolev spaces and crossings between modes at worst conical. show despite singularity they create, conical crossing do not trap prevent dispersion. also investigate interactions can occurred when there some degenerate bands.