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Phases of scrambling in eigenstates
by Tarek Anous, Julian Sonner
This Submission thread is now published as
Submission summary
| Authors (as registered SciPost users): | Tarek Anous · Julian Sonner |
| Submission information | |
|---|---|
| Preprint Link: | https://arxiv.org/abs/1903.03143v3 (pdf) |
| Date accepted: | 2019-06-18 |
| Date submitted: | 2019-06-13 02:00 |
| Submitted by: | Anous, Tarek |
| Submitted to: | SciPost Physics |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
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| Approach: | Theoretical |
Abstract
We use the monodromy method to compute expectation values of an arbitrary number of light operators in finitely excited ("heavy") eigenstates of holographic 2D CFT. For eigenstates with scaling dimensions above the BTZ threshold, these behave thermally up to small corrections, with an effective temperature determined by the heavy state. Below the threshold we find oscillatory and not decaying behavior. As an application of these results we compute the expectation of the out-of-time order arrangement of four light operators in a heavy eigenstate, i.e. a six-point function. Above the threshold we find maximally scrambling behavior with Lyapunov exponent $2\pi T_{\rm eff}$. Below threshold we find that the eigenstate OTOC shows persistent harmonic oscillations.
Author comments upon resubmission
We have addressed the referee’s comments and fixed the two typos they pointed out. We have also seized the opportunity to correct two further minor typos. See list of changes.
Reply to referee:
We would like to thank the referee for their careful reading and insightful report. We reply to their comment as follows:
The referee raises the important point of the validity of the assumption of identity block domination and whether a further hierarchy among the light operators is necessary. Such an additional hierarchy is not necessary for our result to hold, one merely needs to assume that the total contribution to the semiclassical stress tensor coming from the aggregate effect of the Q operators is $O(\varepsilon c)$ in the notation of our paper.
As an example we have shown how to extract the Lyapunov exponent from a six-point function between two heavy and four light operators, with no additional hierarchy between the latter. Nevertheless it would be interesting to investigate if further mileage can be gained from making the additional assumption of such a hierarchy.
List of changes
igure 2: replaced erroneous ‘=' sign with the word ‘operators’.
Page 8, below Eq. (3.10): fixed an incorrect subscript on the matrix $M$.
Top of page 14: we fixed the sentence structure, as pointed out by the referee.
Page 17: minor typo fixed (“does not decays” replaced by “does not decay”).
Published as SciPost Phys. 7, 003 (2019)