arXiv subjects
Publications and source records attributed to Taisuke Yoneyama.
In this paper, we construct a modified wave operators for Schrodinger equations with time-dependent long-range potentials by using wave packet transform and give a proof of the existence of the modified wave operators.
Quadratic repulsive potentials $- τ^2 |x| ^2$ accelerate the quantum particle, increasing the velocity of the particle exponentially in $t$; this phenomenon yields fast decaying dispersive estimates. In this study, we consider the Strichartz estimates associated with this phenomenon. First, we consider the free repulsive Hamiltonian, and prove that the Strichartz estimates hold for every admissible pair $(q,r)$, which satisfies $1/q +n/(2r) \geq n/4$ with $q$, $r \geq 2$. Second, we consider the perturbed repulsive Hamiltonian with a slowly decaying potential, such that $|V(x)| \leq C(1+|x|)^{-δ}$ for some $δ>0$, and prove that the Strichartz estimate holds with the same admissible pairs for repulsive-admissible pairs.
In this paper, we determine the C-infinity type wave front sets of the solutions to the Schrodinger equations with time-dependent variable coefficients and potentials by using the wave packet transform. We introduce the infinite sum and estimate the perturb terms of the flat Laplacian on flat plane, which cannot be estimated by the method in Kato-Ito.
In this paper, we give a characterization of the ranges of the wave operators for Schrodinger equations with time-dependent short-range potentials by using wave packet transform. We also give an alternative proof of the existence of the wave operators for time-dependent potentials and the asymptotic completeness for timeindependent potentials.
In this paper, we consider the existence and the asymptotic completeness of the wave operators for Schrodinger equations with time-dependent potentials which are short-range in space.