Bogolyubov's averaging theorem applied to the Kramers-Henneberger Hamiltonian

TL;DR

This paper applies Bogolyubov's averaging theorem to analyze electron motion in an atom under a laser field within the Kramers-Henneberger frame, providing estimates of trajectory differences and a modified theorem for better accuracy.

Contribution

It introduces a modified Bogolyubov averaging theorem tailored for Hamiltonian systems and assesses the validity of the Kramers-Henneberger approximation in atomic physics.

Findings

Derived estimates of trajectory differences based on laser parameters

Formulated a Hamiltonian-based version of Bogolyubov's theorem

Discussed conditions for the validity of the Kramers-Henneberger approximation

Abstract

We apply Bogolyubov's averaging theorem to the motion of an electron of an atom driven by a linearly polarized laser field in the Kramers-Henneberger frame. We provide estimates of the differences between the original trajectories and the trajectories associated with the averaged system as a function of the parameters of the laser field and the region of phase space. We formulate a modified Bogolyubov averaging theorem based on the Hamiltonian properties of the system, and show that this version is better suited for these systems. From these estimates, we discuss the validity of the Kramers-Henneberger approximation.