Matthias Huebner, Herbert Spohn
Spectral properties of the spin-boson Hamiltonian
(78K, PlainTeX)
ABSTRACT. 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.