The Timescales of Quantum Breaking.

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