  We study the stability of the coherence of a state of a quantum system under
the effect of an interaction with another quantum system at short time. We find
an expression for evaluating the order of magnitude of the time scale for the
onset of instability as a function of the initial state of both involved
systems and of the sort of interaction between them. As an application we study
the spin-boson interaction in the dispersive interaction regime, driven by a
classical field. We find, for this model, that the behavior of the time scale
for the onset of instability, with respect to the boson bath temperature,
changes depending on the intensity of the classical field.
