11/07/2023: Davide Lonigro @ UniMi

July 11, 2023 - 15:00
Sala di Rappresentanza (ground floor on the left)
Mathematics Department, University of Milan
Via Cesare Saldini 50, Milano, Italy

SPEAKER: Davide Lonigro (Università degli Studi di Bari)

Self-adjointness of a class of spinboson models with ultraviolet divergences 

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.