Resolvent smoothness and local decay at low energies for the standard model of non-relativistic QED

TL;DR

This paper proves smoothness of the resolvent and local decay of photon dynamics near the ground state energy in non-relativistic QED, using Mourre theory and Hardy estimates, with results uniform across spectral intervals.

Contribution

It introduces a novel application of Mourre's theory and Hardy estimates to establish resolvent smoothness and decay in the standard non-relativistic QED model.

Findings

Proved resolvent smoothness near the ground state energy.

Established local decay of photon dynamics.

Results are uniform across spectral intervals.

Abstract

We consider an atom interacting with the quantized electromagnetic field in the standard model of non-relativistic QED. The nucleus is supposed to be fixed. We prove smoothness of the resolvent and local decay of the photon dynamics for quantum states in a spectral interval I just above the ground state energy. Our results are uniform with respect to I. Their proofs are based on abstract Mourre's theory, a Mourre inequality established in [FGS1], Hardy-type estimates in Fock space, and a low-energy dyadic decomposition.