13 citations · 36 across the 15 of their papers we have counts for
16 papers
On wave operators for Hardy operators with and without perturbations
Atsuhide Ishida, Konstantin Merz
We prove asymptotic completeness of the wave operators in time-dependent scattering theory which intertwine the ordinary or fractional Laplacian and the corresponding Hardy operato…
Inverse scattering for -body time-decaying harmonic oscillators
Atsuhide Ishida
In the previous study (Ishida, 2025), the author proved the uniqueness of short-range potential functions using the Enss-Weder time-dependent method (Enss and Weder, 1995) for a tw…
Quantum inverse scattering for time-dependent repulsive Hamiltonians of quadratic type
Atsuhide Ishida
We study a multidimensional inverse scattering problem under the time-dependent repulsive Hamiltonians of quadratic type. The time-dependent coefficient on the repulsive term decay…
Special potentials for relativistic Laplacians I: Fractional Rollnik-class
Giacomo Ascione, Atsuhide Ishida, József Lőrinczi
We propose a counterpart of the classical Rollnik-class of potentials for fractional and massive relativistic Laplacians, and describe this space in terms of appropriate Riesz pote…
Inverse scattering for repulsive potential and strong singular interactions
Atsuhide Ishida
In a previous work of 2014 on a quantum system governed by the repulsive Hamiltonian, the author proved uniqueness for short-range interactions described by a scattering operator c…
On Schrödinger equation with square and inverse-square potentials
Atsuhide Ishida, Masaki Kawamoto
In this paper, we study the linear and nonlinear Schrödinger equations with a time-decaying harmonic oscillator and inverse-square potential. This model retains a form of scale inv…
Quantum inverse scattering for time-decaying harmonic oscillators
Atsuhide Ishida
Different from the usual harmonic oscillator, the time-decaying harmonic oscillator accelerates particles and generates scattering states. We study one of the multidimensional inve…
Nonexistence of wave operators via strong propagation estimates for Schrödinger operators with sub-quadratic repulsive potentials
Atsuhide Ishida, Masaki Kawamoto
Sub-quadratic repulsive potentials accelerate quantum particles and can relax the decay rate in the of the external potentials that guarantee the existence of the quantum w…
Absence of Embedded Eigenvalues for Non-Local Schrödinger Operators
Atsuhide Ishida, József Lőrinczi, Itaru Sasaki
We consider non-local Schrödinger operators with kinetic terms given by several different types of functions of the Laplacian and potentials decaying to zero at infinity, and deriv…
Minimal velocity bound for Schroedinger-type operator with fractional powers
Atsuhide Ishida
It is known in scattering theory that the minimal velocity bound plays a conclusive role in proving the asymptotic completeness of the wave operators. In this study, we prove the m…
Threshold between short and long-range potentials for non-local Schrödinger operators
Atsuhide Ishida, Kazuyuki Wada
We develop scattering theory for non-local Schrödinger operators defined by functions of the Laplacian that include its fractional power with . In particula…
Critical scattering in a time-dependent harmonic oscillator
Atsuhide Ishida, Masaki Kawamoto
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…
Inverse scattering in Stark effect
Atsuhide Ishida
We study one of the multidimensional inverse scattering problems for quantum systems governed by the Stark Hamiltonians. By applying the time-dependent method developed by Enss and…
Existence and nonexistence of wave operators for time-decaying harmonic oscillators
Atsuhide Ishida, Masaki Kawamoto
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…
Nonexistence of usual wave operators for fractional Laplacian and slowly decaying potentials
Atsuhide Ishida
We consider quantum systems described by the fractional powers of the negative Laplacian and the interaction potentials. When a slowly decaying potential function is given, we prov…
Propagation property and its application to inverse scattering for fractional powers of the negative Laplacian
Atsuhide Ishida
Enss (1983) proved a propagation estimate for the usual free Schroedinger operator that turned out later to be very useful for inverse scattering in the work of Enss--Weder (1995).…