Pointwise bounds on confined states in non-relativistic QED

TL;DR

This paper extends Kato's inequality to non-relativistic QED, providing new bounds on confined states, including subsolution estimates and exponential decay of eigenstates below the ionization threshold.

Contribution

It generalizes Kato's inequality to vector-valued wave functions in QED and introduces applications for eigenstate bounds and decay estimates.

Findings

Eigenstates satisfy a subsolution estimate

Eigenstates below ionization threshold decay exponentially

Kato's inequality applies to vector-valued wave functions in QED

Abstract

Kato's well known distributional inequality for the magnetic Laplacian holds equally in the more general setting of non-relativistic quantum electrodynamics (QED), where the wave function is vector-valued and the vector potential is quantized. We give two new applications of this result: First, we show that eigenstates satisfy a subsolution estimate. Second, for general states, with energy distribution strictly below the ionization threshold, we give a short proof of pointwise exponential decay in the electronic configuration.