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Traveling discontinuity at the quantum butterfly front
by Camille Aron, Eric Brunet, Aditi Mitra
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|Authors (as registered SciPost users):||Camille Aron|
|Preprint Link:||scipost_202301_00017v1 (pdf)|
|Date submitted:||2023-01-11 15:28|
|Submitted by:||Aron, Camille|
|Submitted to:||SciPost Physics|
We formulate a kinetic theory of quantum information scrambling in the context of a paradigmatic model of interacting electrons in the vicinity of a superconducting phase transition. We carefully derive a set of coupled partial differential equations that effectively govern the dynamics of information spreading in generic dimensions. They exhibit traveling wave solutions that are discontinuous at the boundary of the light cone, and have a perfectly causal structure where the solutions do not spill outside of the light cone.
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Reports on this Submission
- Cite as: Anonymous, Report on arXiv:scipost_202301_00017v1, delivered 2023-02-18, doi: 10.21468/SciPost.Report.6764
The authors studied the out-of-time-ordered correlation function of interacting electrons in the vicinity of the superconductivity phase transition on the disordered side. They used the inter-world kinetic theory on the Keldysh contour to derive a set of coupled differential equations describing information scrambling in the system. This set of coupled differential equations differs from the FKPP equation derived before. The authors found that the equations display a traveling wave solution, and the asymptotic wavefront develops a discontinuity at the wavefront, which is absent in the conventional FKPP equation. The authors also remarked on the possible reasons for the discontinuity, which they left for future study.
The result of the work is interesting because the derived coupled differential equation from the partial wave expansion displays an elegant form and results in interesting wavefront dynamics that have not been studied before. Therefore, the result is worth publishing.
Here are some suggestions for the authors to consider:
1. The authors should explain the role of superconductivity fluctuations and how the vicinity of the phase transition affects the calculation in the introduction. It would also be helpful to explain how the equation would change if the system were far from the phase transition and whether any phase transition fluctuations would lead to the same equation.
2. The authors should relate the inter-world distribution function to OTOC more closely in the summary and main results section. They should also explain how to calculate OTOC from the inter-world distribution function.
3. The calculation was performed at a finite temperature, so the authors should explain how temperature enters the equation.
4. The authors should comment on possible numerical simulations needed to verify the discontinuity in the wavefront.
- Cite as: Anonymous, Report on arXiv:scipost_202301_00017v1, delivered 2023-02-15, doi: 10.21468/SciPost.Report.6748
The authors study a standard probe of scrambling, the so-called out-of-time-ordered correlators (OTOCs) in a model of interacting electrons in the vicinity of a superconducting phase transitions. Within a "many-world", or augmented, Keldysh formalism, they derive a kinetic equation for the so-called inter-world distribution function. The authors then proceed to simplify the latter, obtaining an effective description of the scrambling dynamics in terms of a set of coupled PDEs, which allow for an analytic solution.
From the physical point of view, the authors describe in detail the geometric structure of the OTOC wavefront. Most prominently, they find that the propagating wavefront develops a sharp discontinuity at late time, without any diffusive broadening of the light-cone and with no exponentially decaying tails outside of it. Although this is different from what happens in other models, it is not possible to rule out that this is an effect of the performed approximations, as the authors also discuss. In any case, I find the description of the OTOC wavefront very interesting.
I believe the paper is extremely well written. The motivations and framework are very clear. In addition, while the computations are very technical (and I am not an expert in the specific techniques used), I believe the main logic of the derivations is always easy to grasp. In addition, it is always stated very clearly what the approximations are, and how they could affect the final result (including, for instance, the sharp discontinuity of the OTOC wavefront).
Finally, the topic is certainly timely and of broad interest. For these reasons, I believe this is an excellent submission and I recommend publication of the paper, essentially as is.