On the relation between the magnitude and exponent of OTOCs
Abstract
We derive an identity relating the growth exponent of earlytime OTOCs, the preexponential factor, and a third number called "branching time". The latter is defined within the dynamical meanfield framework, namely, in terms of the retarded kernel. This identity can be used to calculate stringy effects in the SYK and similar models; we also explicitly define "strings" in this context. As another application, we consider an SYK chain. If the coupling strength βJ is above a certain threshold and nonlinear (in the magnitude of OTOCs) effects are ignored, the exponent in the butterfly wavefront is exactly 2 π/β.
 Publication:

Journal of High Energy Physics
 Pub Date:
 February 2019
 DOI:
 10.1007/JHEP02(2019)075
 arXiv:
 arXiv:1812.00120
 Bibcode:
 2019JHEP...02..075G
 Keywords:

 AdSCFT Correspondence;
 1/N Expansion;
 Models of Quantum Gravity;
 High Energy Physics  Theory;
 Condensed Matter  Strongly Correlated Electrons
 EPrint:
 20 pages, 7 figures