Semiclassical wave packet dynamics in Schrodinger equations with   periodic potentials
  We consider semiclassically scaled Schrodinger equations with an external potential and a highly oscillatory periodic potential. We construct asymptotic solutions in the form of semiclassical wave packets. These solutions are concentrated (both, in space and in frequency) around the effective semiclassical phase-space flow obtained by Peierl's substitution, and involve a slowly varying envelope whose dynamics is governed by a homogenized Schrodinger equation with time-dependent effective mass. The corresponding adiabatic decoupling of the slow and fast degrees of freedom is shown to be valid up to Ehrenfest time scales. 
R\'emi Carles (I3M), Christof Sparber (UIC)
math-ph math.AP math.MP