On the Spectral Properties of the Spin-Boson Hamiltonians

Abstract

We analyze the spectral properties of the spin-boson model, describing a two level atom coupled to a boson field. We show that a limiting absorption principle holds, and there is no singularly continuous spectrum for this Hamiltonian outside some small neighborhoods of the eigenvalues of the spin matrix. For this, we construct a conjugate operator for a special class of self-adjoint operators.