July 11, 2023 --- room and time to be determined --- Mathematics Department, University of Milan Via Cesare Saldini 50, Milano, Italy
SPEAKER: Davide Lonigro (Università degli Studi di Bari)
Title: Self-adjointness of a class of spin–boson models with ultraviolet divergences
Abstract: We study a class of quantum Hamiltonian operators describing a family of 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. Starting from the single-atom case, and eventually reaching the general scenario, we shall provide explicit expressions for the self-adjointness domain and the resolvent operator of such models. This construction is also shown to be stable, in the norm resolvent sense, under approximations of the form factors by normalizable ones, for example an ultraviolet cutoff.