arXiv subjects
Publications and source records attributed to Masaki Kawamoto.
Strichartz estimates for a time-decaying harmonic oscillator were proven with some assumptions of coefficients for the time-decaying harmonic potentials. The main results of this paper are to remove these assumptions and to enable us to deal with the more general coefficient functions. Moreover, we also prove similar estimates for time-decaying homogeneous magnetic fields.
In this study, we examine the asymptotic behavior of solutions to nonlinear Schrödinger equations with time-dependent harmonic oscillators and prove the time-decay property of solutions in the case of a long range power type nonlinearity.
Controlled time-decaying harmonic potentials decelerate the velocity of the charged particle but the particle never be trapped by this harmonic potentials. This physical phenomena changes threshold between the short range class of potential and long-range class of potential in the sense of the existence of physical wave operators. In this paper, we reveal such a threshold is $1/(1-λ)$ for some $0\leq λ<1/2$ , which is determined by the mass of the particle and a coefficient of harmonic potential.
We investigate the time propagation of singularity of a solution to linearized KdV equation by using the characterization of wave front sets with using to the wave packet transform (short time Fourier transform).
Controlled time-decaying harmonic oscillator changes the threshold of decay order of the potential functions in order to exist the physical wave operators. This threshold was first reported by Ishida and Kawamoto \cite{IK} for the non-critical case. In this paper we deal with the critical case. As for the critical case, the situation changes drastically, and much more rigorous analysis is required than that of non-critical case. We study this critical behavior and clarify the threshold by the power of the log growth of the potential functions. Consequently, this result reveals the asymptotics for quantum dynamics of the critical case.
By controlling coefficients and decaying order of time-decaying harmonic potentials, the velocity of a quantum particle is decelerated by the effect of harmonic potentials but the particle is non-trapping. In this paper, we consider the quantum system with controlled harmonic potentials. By defining the wave operators for this system and suitable range of these, we can prove the existence and completeness of wave operators with respect to the short-range potentials $V(t,x)$ satisfying $|V(t,x)| = o ((1+|x|)^{-1/(1- λ)})$, for some $λ$, $0< λ< 1/2$.
In this paper, we prove the energy stable property for time-dependent (generalized) Schrödinger operators by using Hardy inequality. Such property acts very important roles in quantum scattering theory and nonlinear problem. As an application, we prove Sobolev type inequality.
We prove the limiting absorption principle on the non-compact interval $I$, on which the uniformly positive Mourre estimate holds. We reveal that such a result yields so-called smoothing estimates.
We study the Mourre theory for the Floquet Hamiltonian $\hat{H} = -i \partial_t + H(t)$ generated by the time-periodic Hamiltonian $H(t)$ with $H(t+T) =H(t)$, which describes the Schrödinger equations with general time-periodic magnetic fields.
We consider a system associated to Klein-Gordon equations with homogeneous time-dependent electric fields. The upper and lower boundaries of a time-evolution propagator for this system were proven by Veselić in 1991 for electric fields that are independent of time. We extend this result to time-dependent electric fields.