  This paper is a companion to 'Quantum Diffusion with Drift and the Einstein
Relation I' (jointly submitted to arXiv). Its purpose is to describe and prove
a certain number of technical results used in 'Quantum Diffusion with Drift and
the Einstein Relation I', but not proven there. Both papers concern long-time
properties (diffusion, drift) of the motion of a driven quantum particle
coupled to an array of thermal reservoirs. The main technical results derived
in the present paper are $(1)$ an asymptotic perturbation theory applicable for
small driving, and, $(2)$ the construction of time-dependent correlation
functions of particle observables.
