We consider a boson system interacting with a heat reservoir in time-dependent external fields which are composed
of a static field and a weak driving field. We take into account the Hamiltonians of the boson system and heat reservoir in
the external static field to be given by the Hamiltonians (2.5), (2.40) and (2.41) in Section 2. We consider the case that the
external driving field is a classical field described by a c-number function of time t and is a periodic function of the frequency
ω, and take the interaction of the boson system with the external driving field as