Existence and nonexistence of wave operators for time-decaying harmonic oscillators

Abstract

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 $1/(1-\lambda )$ for some $0\le \lambda <1/2$ , which is determined by the mass of the particle and a coefficient of harmonic potential.

Cited by in corpus (5)

• Critical scattering in a time-dependent harmonic oscillator
• Strichartz estimates for Schrödinger operators with square potential with time-dependent coefficients
• Final state problem for nonlinear Schrödinger equations with time-decaying harmonic oscillators
• Long-range scattering for a critical homogeneous type nonlinear Schrödinger equation with time-decaying harmonic potentials
• Nonexistence of wave operators via strong propagation estimates for Schrödinger operators with sub-quadratic repulsive potentials