STRUCTURE OF THE EIGENVALUE SPECTRUM IN THE ONE-EXCITATION SUBSPACE OF THE LEE-FRIEDRICHS HAMILTONIAN

The distribution of eigenvalues of the Lee-Friedrichs Hamiltonian in t he continuum limit is attained starting from a finite set of N unpertu rbed field modes. The lowest eigenvalue E(G) is followed as N increase s. As N --> infinity E(G) behaves pathologically while the rest of the spectrum tends to the unperturbed continuum. This behaviour may be at the origin of well-known peculiar features of the spectrum, relevant for quantum optics.