# Energy diffusion and the butterfly effect in inhomogeneous Sachdev-Ye-Kitaev chains

### Submission summary

 As Contributors: Andrew Lucas Arxiv Link: https://arxiv.org/abs/1702.08462v2 (pdf) Date accepted: 2017-05-11 Date submitted: 2017-05-10 02:00 Submitted by: Lucas, Andrew Submitted to: SciPost Physics Academic field: Physics Specialties: Condensed Matter Physics - Theory High-Energy Physics - Theory Approach: Theoretical

### Abstract

We compute the energy diffusion constant $D$, Lyapunov time $\tau_{\text{L}}$ and butterfly velocity $v_{\text{B}}$ in an inhomogeneous chain of coupled Majorana Sachdev-Ye-Kitaev (SYK) models in the large $N$ and strong coupling limit. We find $D\le v_{\text{B}}^2 \tau_{\text{L}}$ from a combination of analytical and numerical approaches. Our example necessitates the sharpening of postulated transport bounds based on quantum chaos.

### Ontology / Topics

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Published as SciPost Phys. 2, 018 (2017)

We thank the referees for their positive feedback. We have edited the manuscript along the lines suggested -- see the list of changes. We hope that these changes satisfy the referees and the paper can be published in its present form.

### List of changes

1) We have added Reference 12 in the introduction as an example of a violation of a postulated relation between charge diffusion and v_B.

2) We have modified the main text in Section 2 around Equations 7-11, along with adding a new Appendix, in order to address a referee's concern that our derivation of the effective action should be more self-contained.