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

## TL;DR

This paper investigates energy transport and chaos in an inhomogeneous SYK chain, revealing bounds on diffusion and chaos parameters that challenge existing transport bounds based on quantum chaos.

## Contribution

It provides analytical and numerical analysis of energy diffusion, Lyapunov time, and butterfly velocity in an inhomogeneous SYK chain, highlighting the need to refine chaos-based transport bounds.

## Key findings

- Energy diffusion constant D computed and bounded by v_B^2 τ_L
- Demonstration that D ≤ v_B^2 τ_L in the model
- Necessity to sharpen quantum chaos-based transport bounds

## 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.