Self-adjointness of a class of multi-spin-boson models with ultraviolet divergences

Abstract

We study a class of quantum Hamiltonian models describing a family of $N$ two-level systems (spins) coupled with a structured boson field of positive mass, with a rotating-wave coupling mediated by form factors possibly exhibiting ultraviolet divergences (hence, non-normalizable). Spin-spin interactions which do not modify the total number of excitations are also included. Generalizing previous results in the single-spin case, we provide explicit expressions for the self-adjointness domain and the resolvent operator of such models, both of them carrying an intricate dependence on both the spin-field and spin-spin coupling via a family of concatenated propagators. This construction is also shown to be stable, in the norm resolvent sense, under approximations of the form factors via normalizable ones, for example an ultraviolet cutoff.

17 pages; close to published version. v3: typos corrected

References in corpus (6)

• Photon-mediated interactions between distant artificial atoms
• Dynamics of spontaneous emission in a single-end photonic waveguide
• On Existence of Ground States in the Spin Boson Model
• Self-Adjointness criterion for operators in Fock spaces
• Generalized spin-boson models with non-normalizable form factors
• The self-energy of Friedrichs-Lee models and its application to bound states and resonances

Cited by in corpus (6)

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• Self-adjointness and domain of generalized spin-boson models with mild ultraviolet divergences
• On the resolvent of $H+A^{\ast }+A$