Asymptotic completeness of wave operators for Schr\"{o}dinger operators with time-periodic magnetic fields

TL;DR

This paper proves the asymptotic completeness of wave operators for Schrödinger operators with more general and optimal time-periodic magnetic fields, including uniform resolvent estimates for the Floquet Hamiltonian.

Contribution

It relaxes previous restrictions on magnetic fields and wave operator ranges, establishing more general conditions for asymptotic completeness.

Findings

Asymptotic completeness established under generalized magnetic field conditions

Uniform resolvent estimates for the perturbed Floquet Hamiltonian obtained

Results extend previous work by removing restrictive assumptions

Abstract

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.