  Due to the inevitable existence of quantum effects, a classical description
generically breaks down after a finite quantum break-time $t_q$. We aim to find
criteria for determining $t_q$. To this end, we construct a new prototype model
that features numerous dynamically accessible quantum modes. Using explicit
numerical time evolution, we establish how $t_q$ depends on the parameters of
the system such as its particle number $N$. The presence of a classical
instability leads to $t_q \sim \ln N$ or $t_q\sim \sqrt{N}$. In the stable
case, we observe $t_q\sim N$, although full quantum breaking may not take place
at all. We find that the different regimes merge smoothly with $t_q\sim
N^\gamma$ ($0<\gamma<1$). As an outlook, we point out possibilities for
transferring our results to black holes and expanding spacetimes.
