Effective density of states for a quantum oscillator coupled to a photon field

TL;DR

This paper derives an explicit formula for the effective partition function of a quantum harmonic oscillator coupled to a photon field, revealing its spectral properties and resonances through complex analysis.

Contribution

It provides a novel explicit formula for the effective partition function and characterizes the spectral resonances of a quantum oscillator-photon system.

Findings

Effective partition function expressed as Laplace transform of a positive measure

Identification of resonances as singularities approximated by first order poles

Complete analytic description of the oscillator's natural line spectrum

Abstract

We give an explicit formula for the effective partition function of a harmonically bound particle minimally coupled to a photon field in the dipole approximation. The effective partition function is shown to be the Laplace transform of a positive Borel measure, the effective measure of states. The absolutely continuous part of the latter allows for an analytic continuation, the singularities of which give rise to resonances. We give the precise location of these singularities, and show that they are well approximated by of first order poles with residues equal the multiplicities of the corresponding eigenspaces of the uncoupled quantum oscillator. Thus we obtain a complete analytic description of the natural line spectrum of the charged oscillator.