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.

arXiv comment17 pages; close to published version. v3: typos corrected

References in corpus (21)

• Photon-mediated interactions between distant artificial atoms
• The role of the rigged Hilbert space in Quantum Mechanics
• Laser driven atoms in half-cavities
• Dynamics of spontaneous emission in a single-end photonic waveguide
• Bound states and entanglement generation in waveguide quantum electrodynamics
• Reliable multiphoton generation in waveguide QED
• Dynamical signatures of bound states in waveguide QED
• Bound states in the continuum for an array of quantum emitters
• On Nelson-type Hamiltonians and abstract boundary conditions
• Self-Adjointness and Domain of the Froehlich Hamiltonian
• Avoiding Ultraviolet Divergence by Means of Interior-Boundary Conditions
• On the domain of the Nelson Hamiltonian
• Particle Creation at a Point Source by Means of Interior-Boundary Conditions
• Hamiltonians Without Ultraviolet Divergence for Quantum Field Theories
• On Existence of Ground States in the Spin Boson Model
• Feynman-Kac formulas for the ultra-violet renormalized Nelson model
• Self-Adjointness criterion for operators in Fock spaces
• Generalized spin-boson models with non-normalizable form factors
• On the self-adjointness of H+A*+A
• The self-energy of Friedrichs-Lee models and its application to bound states and resonances
• Existence of Resonances for the Spin-Boson-Model with Critical Coupling Function

Cited by in corpus (6)

• Ultrastrong coupling, nonselective measurement and quantum Zeno dynamics
• Efficiency of Dynamical Decoupling for (Almost) Any Spin-Boson Model
• Extended State Space for describing renormalized Fock spaces in QFT
• Quasi-classical Limit of a Spin Coupled to a Reservoir
• Self-adjointness and domain of generalized spin-boson models with mild ultraviolet divergences
• On the resolvent of $H+A^{\ast }+A$