Generalized spin-boson models with non-normalizable form factors

Abstract

Generalized spin-boson (GSB) models describe the interaction between a quantum mechanical system and a structured boson environment, mediated by a family of coupling functions known as form factors. We propose an extension of the class of GSB models which can accommodate non-normalizable form factors, provided that they satisfy a weaker growth constraint, thus accounting for a rigorous description of a wider range of physical scenarios; we also show that such "singular" GSB models can be rigorously approximated by GSB models with normalizable form factors. Furthermore, we discuss in greater detail the structure of the spin-boson model with a rotating wave approximation (RWA): for this model, the result is improved via a nonperturbative approach which enables us to further extend the class of admissible form factors, as well as to compute its resolvent and characterize its self-adjointness domain.

40 pages; new section added

References in corpus (9)

• Dressed Collective Qubit States and the Tavis-Cummings Model in Circuit QED
• The quantum Rabi model: solution and dynamics
• Mesoscopic Spin-Boson Models of Trapped Ions
• Quantification of memory effects in the spin-boson model
• Quantum regression beyond the Born-Markov approximation for generalized spin-boson models
• Quantum regression in dephasing phenomena
• On Existence of Ground States in the Spin Boson Model
• Self-Adjointness criterion for operators in Fock spaces
• The self-energy of Friedrichs-Lee models and its application to bound states and resonances

Cited by in corpus (9)

• Quantum regression in dephasing phenomena
• On Markovianity and classicality in multilevel spin-boson models
• Self-adjointness of a class of multi-spin-boson models with ultraviolet divergences
• Ultrastrong coupling, nonselective measurement and quantum Zeno dynamics
• Extended State Space for describing renormalized Fock spaces in QFT
• Efficiency of Dynamical Decoupling for (Almost) Any Spin-Boson Model
• Renormalization of spin$\unicode{x2013}$boson interactions mediated by singular form factors
• Self-adjointness and domain of generalized spin-boson models with mild ultraviolet divergences
• Quasi-classical Limit of a Spin Coupled to a Reservoir