Asymptotic completeness of wave operators for Schrödinger operators with time-periodic magnetic fields

Masaki Kawamoto

Published 2021-05-13, updated 2021-05-25Version 2

Under the effect of suitable time-periodic magnetic fields, the velocity of a charged particle grows exponentially in $t$; this phenomenon provides the asymptotic completeness for wave operators with slowly decaying potentials. These facts were shown under some restrictions for time-periodic magnetic fields and the range of wave operators. In this study, we relax these restrictions and finally obtain the asymptotic completeness of wave operators. Additionally, we show them under generalized conditions, which are truly optimal for time-periodic magnetic fields. Moreover, we provide a uniform resolvent estimate for the perturbed Floquet Hamiltonian.