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arXiv · 2109.02939

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

Davide Lonigro
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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.

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Davide Lonigro. 2021-09-07. The self-energy of Friedrichs-Lee models and its application to bound states and resonances. https://doi.org/10.1140/epjp%2Fs13360-022-02690-y

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