Mourre Theory For Time-Periodic Magnetic Fields

TL;DR

This paper develops Mourre theory for Floquet Hamiltonians associated with Schrödinger equations under general time-periodic magnetic fields, providing a framework to analyze their spectral properties.

Contribution

It extends Mourre theory to time-periodic magnetic fields, offering new tools for spectral analysis of Floquet Hamiltonians in quantum mechanics.

Findings

Established Mourre estimates for Floquet Hamiltonians with magnetic fields.

Provided spectral analysis techniques for time-periodic quantum systems.

Enhanced understanding of the spectral properties of Schrödinger operators with magnetic fields.

Abstract

We study the Mourre theory for the Floquet Hamiltonian $\hat{H} = -i \partial_t + H(t)$ generated by the time-periodic Hamiltonian $H(t)$ with $H(t+T) =H(t)$, which describes the Schr\"{o}dinger equations with general time-periodic magnetic fields.