Spectral properties of the singular Friedrichs-Lee Hamiltonian

TL;DR

This paper generalizes the Friedrichs-Lee model to include singular atom-field couplings, characterizes its spectrum and resonances, and explores the inverse spectral problem, advancing understanding of atom-field interactions.

Contribution

It introduces a generalized Friedrichs-Lee model with singular couplings, providing new spectral and resonance analysis methods.

Findings

Characterization of the spectrum of the generalized model

Analysis of resonances in the singular coupling case

Discussion of the inverse spectral problem for the model

Abstract

We show that the Friedrichs-Lee model, which describes the one-excitation sector of a two-level atom interacting with a structured boson field, can be generalized to singular atom-field couplings. We provide a characterisation of its spectrum and resonances and discuss the inverse spectral problem.