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arXiv · 2111.06121

Generalized spin-boson models with non-normalizable form factors

Davide Lonigro
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Abstract

Generalized spin-boson (GSB) models describe the interaction between a quantum mechanical system and a structured boson environment, mediated by a family of coupling functions known as form factors. We propose an extension of the class of GSB models which can accommodate non-normalizable form factors, provided that they satisfy a weaker growth constraint, thus accounting for a rigorous description of a wider range of physical scenarios; we also show that such "singular" GSB models can be rigorously approximated by GSB models with normalizable form factors. Furthermore, we discuss in greater detail the structure of the spin-boson model with a rotating wave approximation (RWA): for this model, the result is improved via a nonperturbative approach which enables us to further extend the class of admissible form factors, as well as to compute its resolvent and characterize its self-adjointness domain.

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BibTeXRIS

Davide Lonigro. 2021-11-11. Generalized spin-boson models with non-normalizable form factors. https://doi.org/10.1063/5.0085576

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