  We present an exactly solvable model of a hybrid quantum-classical system of
a Nitrogen-Vacancy (NV) center spin (quantum spin) coupled to a nanocantilever
(classical) and analyze the enforcement of the regular or chaotic classical
dynamics onto the quantum spin dynamics. The main problem we focus in this
paper is whether the classical dynamical chaos may induce chaotic effects in
the quantum spin dynamics or not. We explore several characteristic criteria of
the quantum chaos, such as quantum Poincar\'{e} recurrences, generation of
coherence and energy level distribution and observe interesting chaotic effects
in the spin dynamics. Dynamical chaos imposed in the cantilever dynamics
through the kicking pulses induces the stochastic dynamics on the quantum
subsystem. We consider a quantum system of two and three levels and show that
in a two-level case, type of stochasticity is not conforming all the
characteristic features of the quantum chaos and is distinct from it. We also
explore the effect of quantum feedback on dynamics of the cantilever and the
entire system.
