Early-time and late-time quantum chaos
Abstract
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 noninteracting 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.
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