Spin boson model and quantum Rabi model

We talk about the spin-boson model and its one-mode version the "Rabi-model".  Both describe a two level atom linearly interacting with photons. 

By the eigenvalues of the Rabi Hamiltonian,  we can define the spectral zeta function which is indexed by the coupling constant $g$ of the Rabi Hamiltonian. We discuss the asymptotic behavior of the spectral zeta function as $g$ goes to infinity.  For the spin-boson model we discuss the properties of ground state by path measures, and a van Hove representation is given.