The self-energy of Friedrichs-Lee models and its application to bound states and resonances

TL;DR

This paper derives an analytic expression for the self-energy in Friedrichs-Lee models, enabling detailed analysis of bound states and resonances in systems of two-level entities interacting with a bosonic field.

Contribution

It provides a general analytic formula for the self-energy in Friedrichs-Lee models and applies it to analyze bound states and resonances, especially for identical two-level systems.

Findings

Derived a universal analytic expression for the self-energy.

Identified dominant and suppressed contributions to the self-energy.

Explored bound state phenomenology with a single dominant contribution.

Abstract

A system composed of two-level systems interacting with a single excitation of a one-dimensional boson field with continuous spectrum, described by a Friedrichs (or Friedrichs-Lee) model, can exhibit bound states and resonances; the latter can be characterized by computing the so-called self-energy of the model. We evaluate an analytic expression, valid for a large class of dispersion relations and coupling functions, for the self-energy of such models. Afterwards, we focus on the case of identical two-level systems, and we refine our analysis by distinguishing between dominant and suppressed contributions to the associated self-energy; we finally examine the phenomenology of bound states in the presence of a single dominant contribution.