Finite temperature corrections to chaotic models in and out of equilibrium

There has been a renewed interest in chaotic quantum models, motivated by developments in both condensed matter and quantum gravity, as well as the introduction of the now paradigmatic solvable example, the Sachdev-Ye-Kitaev (SYK) ensemble. The low temperature limits of this model and its generalizations have provided key insight into the behaviour of strongly coupled quantum systems, and have served as quantitative proofs of concept for protocols to probe and control them. The understanding of these effects is informed by a dual gravitational description, which has inspired generalizations with surprising properties such as recurrences and arresting thermalization with a drive. By going beyond the low temperature limit in these models in and out of equilibrium, we show that high temperature corrections actually have important qualitative effects that persist in the low temperature limit. We discuss how the dual description has to be modified and the consequences of these modifications to the physics of SYK-like models.