Davide Lonigro
Published 2023-01-25Version 1
We study a class of quantum Hamiltonian models describing a family of $N$ two-level systems (spins) coupled with a structured boson field, 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.
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Self-adjointness and domain of generalized spin-boson models with mild ultraviolet divergences
On higher-dimensional superintegrable systems: A new family of classical and quantum Hamiltonian models
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