On multidimensional inverse scattering in time-dependent electric fields

We study one of the multidimensional inverse scattering problems for quantum systems in time-dependent electric fields E(t), which is represented as E₀(1 + |t|)^-μ with 0 μ < 1, based on the Enss-Weder time-dependent method. We show that when the space dimension is greater than or equal to 2, the high velocity limit of the scattering operator determines uniquely the short-range part like |x|^-γ with γ > 1/(2 - μ) of the potential belonging to the class rather wider than the one given by Adachi, Kamada, Kazuno and Toratani. Our method can also improve previous results in the case where E(t) is periodic in t with non-zero mean E₀.