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

• URL: http://arxiv.org/abs/2109.02939v2
• Date: Tue, 5 Apr 2022 07:40:59 GMT
• Title: The self-energy of Friedrichs-Lee models and its application to bound states and resonances
• Authors: Davide Lonigro
• Abstract summary: Two-level systems interacting with a single excitation of a boson field with continuous spectrum can exhibit bound states and resonances. We evaluate an analytic expression, valid for a class of dispersion relations and coupling functions, for the self-energy of such models. We examine the phenomenology of bound states in the presence of a single dominant contribution.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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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