Regularity and Decay of Solutions to the Stark Evolution Equation

Long-time behavior and regularity are studied for solutions of the Stark equationut=i(−Δ−x1+V(x)) u,u(0, x)∈L2(Rn). It is shown that for a class of short-range potentialsV(x) the gain of local smoothness and the decay as |t|→∞ are close to those of the corresponding Schrödinger equationut=i(−Δ+V(x)) u.