Scrambling versus relaxation in Fermi and non-Fermi liquids

We compute the Lyapunov exponent characterizing quantum scrambling in a family of generalized Sachdev-Ye-Kitaev models, which can be tuned between different low temperature states from Fermi liquids, through non-Fermi liquids to fast scramblers. The analytic calculation, controlled by a small coupling constant and large N allows us to clarify the relations between the quasi-particle relaxation rate 1/\tauand the Lyapunov exponent...