Perturbation theory of a dissipative quantum subsystem

It is shown how a nondegenerate quantum perturbation of a dissipative quantum subsystem, part of a larger conservative system, may be carried out. Under a certain condition, an approximately conservative system may result from adding the perturbation, or equivalently the interactions with the full system. For large systems, the condition leads to nonlinear integral equations and induced gap behaviour in the spectrum. Conditions under which the equations may be satisfied are discussed.