Spectral properties of the spin-boson Hamiltonian

We consider a two level atom coupled to the radiation field. Using a Mourre type estimate, we provide a complete spectral characterization of the spin-boson Hamiltonian for sufficiently small, but nonzero coupling. In particular, the singular continuous spectrum is empty and the point spectrum consists only of the ground state energy. Technically we prove an extension of the Mourre estimate to a conjugate operator which is the generator of an isometry semigroup only. We illustrate such a technique for the Friedrichs model and apply it also to the rotating wave approximation of the spin-boson model.

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