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

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.