  We show the relation between the Heisenberg averaging of regularized 2-point
out-of-time ordered correlation function and the 2-point spectral form factor
in bosonic quantum mechanics. The generalization to all even-point is also
discussed. We also do the direct extension from the bosonic quantum mechanics
to the non-interacting scalar field theory. Finally, we find that the coherent
state and large-$N$ approaches are useful in the late-time study. We find that
the computation of the coherent state can be simplified by the Heisenberg
averaging. Therefore, this provides a simplified way to probe the late-time
quantum chaos through a coherent state. The large-$N$ result is also comparable
to the $N=3$ numerical result in the large-$N$ quantum mechanics. This can
justify that large-$N$ technique in bosonic quantum mechanics can probe the
late time, not the early time. Because the quantitative behavior of large-$N$
can be captured from the $N=3$ numerical result, the realization in experiments
should be possible.
