Critical scattering in a time-dependent harmonic oscillator

Abstract

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.

References in corpus (2)

• Existence and nonexistence of wave operators for time-decaying harmonic oscillators
• Quantum scattering with time-decaying harmonic oscillators

Cited by in corpus (3)

• Long-range scattering for a critical homogeneous type nonlinear Schrödinger equation with time-decaying harmonic potentials
• Asymptotic behavior for nonlinear Schrödinger equations with critical time-decaying harmonic potential
• Nonexistence of wave operators via strong propagation estimates for Schrödinger operators with sub-quadratic repulsive potentials