Approach to ground state and time-independent photon bound for massless spin-boson models

TL;DR

This paper proves relaxation to the ground state and bounds on emitted photons for a finite-level atom interacting with a massless electromagnetic field, advancing understanding of quantum relaxation and photon emission.

Contribution

It provides the first partial proof of relaxation to the ground state and photon bounds for massless spin-boson models with finite-level atoms, under certain regularity conditions.

Findings

Relaxation to an invariant state is proven for finite-level systems.

If the coupling is sufficiently infrared-regular, the invariant state is the ground state.

The number of emitted photons remains bounded over time under additional regularity assumptions.

Abstract

It is widely believed that an atom interacting with the electromagnetic field (with total initial energy well-below the ionization threshold) relaxes to its ground state while its excess energy is emitted as radiation. Hence, for large times, the state of the atom+field system should consist of the atom in its ground state, and a few free photons that travel off to spatial infinity. Mathematically, this picture is captured by the notion of asymptotic completeness. Despite some recent progress on the spectral theory of such systems, a proof of relaxation to the ground state and asymptotic completeness was/is still missing, except in some special cases (massive photons, small perturbations of harmonic potentials). In this paper, we partially fill this gap by proving relaxation to an invariant state in the case where the atom is modelled by a finite-level system. If the coupling to the field is sufficiently infrared-regular so that the coupled system admits a ground state, then this invariant state necessarily corresponds to the ground state. Assuming slightly more infrared regularity, we show that the number of emitted photons remains bounded in time. We hope that these results bring a proof of asymptotic completeness within reach.