  In the framework of simple spin-boson Hamiltonian we study an interplay
between dynamic and spectral roots to stochastic-like behavior. The Hamiltonian
describes an initial vibrational state coupled to discrete dense spectrum
reservoir. The reservoir states are formed by three sequences with rationally
independent periodicities typical for vibrational states in many nanosize
systems. We show that quantum evolution of the system is determined by a
dimensionless parameter which is characteristic number of the reservoir states
relevant for the initial vibrational level dynamics. Our semi-quantitative
analytic results are confirmed by numerical solution of the equation of motion.
We anticipate that predicted in the paper both kinds of stochastic-like
behavior (namely, due to spectral mixing and recurrence cycle dynamic mixing)
can be observed by femtosecond spectroscopy methods in nanosystems.
