I will give an introduction to the physics of the Sachdev-Ye-Kitaev (SYK) model and its chaotic properties in the first part of the talk.
In the second part of the talk, I will consider the kinetic properties in a lattice extension of the SYK model with a quadratic perturbation at an arbitrary frequency and momentum. It will be shown that fluctuations significantly change the kinetic properties at a sufficiently low temperature. I also show the existence of the "zero-sound"-like mode in the model.
The third part is devoted to the study of the out-of-time-order correlation function (OTOC) in the model on the lattice. The results obtained are valid for arbitrary time scales, both shorter and longer than the Ehrenfest time. I demonstrated that the region of well-developed chaos is separated from the weakly chaotic region by the "front region", which moves ballistically across the lattice. Front velocity is calculated for various system parameters, for the first time for SYK-like models.
The talk is based on the following two articles:
 A.V. Lunkin, M.V. Feigel'man, "High-frequency transport and zero-sound in an array of SYK quantum dots", SciPost Physics 13 (3), 073
 A.V. Lunkin, "Butterfly Effect in a System of Quantum Dots in the Sachdev–Ye–Kitaev Model", JETP Letters 115 (5), 297-304